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All Rights Reserved. 11 dict begin /FontInfo 7 dict dup begin /version (2.1) readonly def /Notice (Copyright (C) 1997 American Mathematical Society. All Rights Reserved) readonly def /FullName (MSBM10) readonly def /FamilyName (Euler) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def end readonly def /FontName /CGTGIN+MSBM10 def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 82 /R put dup 90 /Z put readonly def /FontBBox{-55 -420 2343 920}readonly def currentdict end currentfile eexec oc;j~EЪ*BgNӽ ؑlKq*޲Xws|QFqv`zXMyp"5O˩YŝP(DT![v67XFlU&3!Rq4wσ~j+ou\ʻjf 2mC+ KVŘ31 xb1݅67Â->s[$b}=UB3]6mY>/i2v| /Odok YFԝyQjY(_6L(+"#H)_T\ ( ;^͞ŅCW97#[&W(!9?P[Y`f\NWN n! FG߲gMQy5E٫eE~N|ɻa3^'W>B]LaoS aLdy+!B0mύ7d{6˺78Y"ݛc~GeÅ\ ){a%n9ۼPX x?y$h+tP0IS5Hdn*å 7^0ҺX՗x@1&m/GŃӹ`ح+PQN9/-}taަ7;_u K{[[6_Dq)̝hܥI 3XAx˗4DoGx٠UIr?yEuaɳ[XI^D,B`~0Րd߭QmDt㸜Ԝ`3.+ta63grXտݗlWk56FIx}Lc%asDI͟CFpoZ<0 ȒJ~$,t]=fz9faR@dp en#=u/9wlYPMt>f)ht0Y 7iS,!\gm'kk=%?]ORCԏ"?TH?|endstream endobj 460 0 obj <> endobj 461 0 obj [ 550 541 528 628 510 476 593 669 316 307 574 455 822 652 611 520 618 562 464 479 ] endobj 462 0 obj <> endobj 463 0 obj <>stream %!PS-AdobeFont-1.0: t1-gul-regular-smallcaps 001.001 %%Title: t1-gul-regular-smallcaps %Version: 001.001 %%CreationDate: Mon May 26 10:39:46 2008 %%Creator: CV Radhakrishnan,,, %Copyright: Gulliver, Giant amongst Dwarfs. %Copyright: This typeface offers excellent readability at very small %Copyright: sizes. %Copyright: %Copyright: The digitally encoded machine readable outline data for %Copyright: producing the typefaces licensed to you is copyrighted (c), %Copyright: 1994, 2005 by and the property of Gerard Unger. % Generated by FontForge 20070607 (http://fontforge.sf.net/) %%EndComments FontDirectory/t1-gul-regular-smallcaps known{/t1-gul-regular-smallcaps findfont dup/UniqueID known{dup /UniqueID get 4084430 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 12 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /QDTHNW+t1-gul-regular-smallcaps def /FontBBox {-115 -321 1407 1009 }readonly def /UniqueID 4084430 def /XUID [1021 992 867865856 15320446] def /PaintType 0 def /FontInfo 11 dict dup begin /version (001.001) readonly def /Notice (Gulliver, Giant amongst Dwarfs.\012This typeface offers excellent readability at very small sizes.\012\012The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted \050c\051, 1994, 2005 by and the property of Gerard Unger.) readonly def % Gulliver, Giant amongst Dwarfs. % This typeface offers excellent readability at very small sizes. % % The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted (c), 1994, 2005 by and the property of Gerard Unger. /FullName (Gulliver SCOsF) readonly def /FamilyName (Gulliver SCOsF) readonly def /Weight (Regular) readonly def /FSType 4 def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -75 def /UnderlineThickness 50 def /ascent 789 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 97 /a put dup 98 /b put dup 99 /c put dup 101 /e put dup 102 /f put dup 105 /i put dup 108 /l put dup 110 /n put dup 111 /o put dup 114 /r put dup 115 /s put dup 116 /t put readonly def currentdict end currentfile eexec oc;jAw-36Uu4 l.Nk48DPh>[ME7wk9B.H.CSoZqO O)9OHl~Q:ɾD0j J'JZ `B 5ԆG tbY7:Ϳ2hK@,'$Qr[GB_720 qs`a|Xu\ӅZ?.PcN7.?WֺYq^$^VA7Up c?{RlG9a% #SȣP^-qTo8g^Z#Z #v.Cows?**hfy&;D bÍ!*=8-T9wPa4ԩ^vqB }p ;?IX`D-5 %[!Ӟ1o gn/yhgD`Ce}zB-8Zvʼ-ki8˹HCW*e*~V7gHmWrM)OlPlSN hUGXǧ=v%vӈ ^o66'%&AT( uw7 :L{|&( ,cY44rf*go&z* {NhJl0r1xР%syX\8 ]n`85˲#sBIr:lr܎eǪ7o~!sPAz18xA նNthTw6I[T]`T: v5Z*nZ o)f{H0jer9;Q"}l|a/osARS#݅mrnWe$h1Љ^XY{c+qi|l#mH PJ uSCB`ְ{FflVηiޢɊڿ;%rh0x 1y=XZ |~{rwy)&W$.6K6'ؘǿ6BA%dד\vu;7w}`-!/@ )$9vg޽ȭ2,8tv"# 3 $Buw`f aMG8aOһYbI#mM E.i [qI]4>stU'5upLQvE\ oG~$T2i=$v>ÅN.ȿ&6 ?XxKBal߉X+ıybhrm:dïi9 s܋J`I>:X|xE6l">\#M^>)Ʋ}}s14_;ũ yW-D}#/WML윰k7q7t>O@tlӱ%@WǼD^P ;1 ہZU0jm b{e(zaX ,9s~ƣK ͔?;8C=" C; jc: vhu"w@<]Lجt^}2 ԍnK^j*-FK8:s FBJ27+EP A@F''` H+O 9kI^SL<}Ir>4P :)H1䁜ž5[_RUCAxl=_0 p#ks-K~'G OS@~zk9j?qeVp9rAOAM;n] @`}Bx*QVO9_y|=I_ 8ȅQ({KqKbAanm *.Jh-a~Q&wiܪtP*AH)Hk&E}ZOmzMo\ ּ]8JvxJdo_P lz*o{ۡjWհ#GMN].ɨ2e'%_P2̬W'MPAYQps]_HNs&zt~몙~?K _̤H4GyV(Akj.Q䐧HJ:ux\jLFzoSﴔd!в.- cmnWċַ|Flb`.Tv#HYB\)UґV:ҳ?v?&$AOF GlxbF(qfƂgR]8vWJ7krx7M dyF#qgݸts5r ֤cLm3+NW0: )AI!%A7vac;2FERVނGdE90N!tʆH7l#V]^%2ShԿ CΟ^c.2 ),vo,{(ݞK:LlwM 2Y_?l6EPA>YlQP?7Q%1bt [-F˕<1BoqH D'sRrz,Ռbct"׳1&&3e"G Ƙ# 6|a.T_gCAkm z0Hy-~D"i/3SQEfab6ttMgVMvqZ{."3&Wּ-K$IOɢgz3],tG x֪!K3s(r;h[;pq[^[El2J%HZ9pQAQ7?k11gEbc+ktZE XxKBE{6tNa RSmBD}Dpft d+\|ɃVS+C.5c5 :Mhsė Sc흢ܬJfKMمS*)HÑTۈ~;|ӖJU\5a5=i=ljBDxq!X ̦vJp/Y]D0T Sr;y7}{"NV!![‡M[,jzyhWe lUbڌAz*Bנ/#U/qۏ_ހRVAiR2MO.]LaiN+Uzczi :`vrtWA%FNtQQ:_!؊H ;`C=K-վ3$$qStV,O*;Ky󝳻|l8D0@,e9dvfCS:L7و_X[݇0nc]W3[@gN:hV\LY6vNQXPoRUcc߃'LMs!s'%Rᄟ~lfhQDLn7E P\O%9Tj]|Fe/2͹R tَ@9.-~Rxը /W)Jq4ԓˮbd|)#MV;lY p%9ǖq /s} œ8L6&Pzb G:&=W5F$h1Z~ :txkOk"X%.(AZ(1cH }C}X~cR [`?ձ\c %4ƫ/ 7kct=!Zɸ"/[818!tqxQq}([`$6ɨ߂G*9tH戥>M/&.+MtG1MG(\8f#7p85 MfƭlO8'eq*5ƝDV47L8sZu\ƿ qP~5r{P|)q EDsɺ Yɇ[WSbOH,ƞۏ VF4V Zܰn .ow_吵: %<*Y/sP`6#hlWg6Y i*)fySc[-5GwoK=Ɔ`7%(F`G_\? &A_^7` ڞx᧓1S>%!h< D?AfL̢o}P< 3Zq{BZKAM b&<夔3@s"f_t,בwAˇ-,EK)$6ôOi]KсylZ~ nYNLNbXƻ0Jw,BTHgђSD-\fXC#pZ_&0L:ᓎ0_eW^]ԑŲ]b:LQFWIurV~W=dH#*7Ѷݎ&Z5˫wƮ3o{ GP AzܿBK>&Q]V[:]Fq%ac7xStGp w eꅟ87>d& P(y*{j30ˤ~4G_9&^:]R TQ9&e@as`ij5W=\5< ׃`KD ЗS#| )""9[]?ç!,>(;$+IKr? TR'g>NPl`6CmQ{,%>rtFz=1sQ^TfMpδ7W$WBB#~%jĸendstream endobj 464 0 obj <> endobj 465 0 obj [ 790 ] endobj 466 0 obj <> endobj 467 0 obj <>stream %!PS-AdobeFont-1.0: t1-gul-symbol 001.000 %%Title: t1-gul-symbol %Version: 001.000 %%CreationDate: Mon May 12 14:48:11 2008 %%Creator: CV Radhakrishnan,,, %Copyright: Created by CV Radhakrishnan,,, with FontForge 2.0 %Copyright: (http://fontforge.sf.net) % 2008-5-12: Created. % Generated by FontForge 20070607 (http://fontforge.sf.net/) %%EndComments FontDirectory/t1-gul-symbol known{/t1-gul-symbol findfont dup/UniqueID known{dup /UniqueID get 4083185 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 12 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /HWNAVD+t1-gul-symbol def /FontBBox {5 -213 895 789 }readonly def /UniqueID 4083185 def /XUID [1021 992 867865827 11599217] def /PaintType 0 def /FontInfo 9 dict dup begin /version (001.000) readonly def /Notice (Created by CV Radhakrishnan,,, with FontForge 2.0 \050http://fontforge.sf.net\051) readonly def /FullName (t1-gul-symbol) readonly def /FamilyName (t1) readonly def /Weight (Medium) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 39 /copyright put readonly def currentdict end currentfile eexec oc;jAw-6n}H#vݟ~Lڎko:FVvixؕBv0_ dĮ&8`}-AʌOǦ\Q]&8~a0[V2v)}H6p4aDPf0?IGrq㋒nDJ,52 HEh M/Z1hR 3 |/AF>"T6`~yxd<^;CNJ idjITR⏢Ɂw'ƺVTqرޡc%C TQIC:/*nX̅M}1ba) /h6A!7\PG|~zh~8^8s!BMYI:ꓩua!7h*){7sw2zI۳V,DK-yp~ONi8&ǁHkZr!U-UlM2U6cN=h",Η`%-9 5DpHa>-YÜbh@@XfY|M#X žendstream endobj 468 0 obj <> endobj 469 0 obj [ 622 792 788 796 764 820 798 651 764 686 827 571 564 502 430 437 430 520 440 300 492 547 686 472 426 600 545 534 433 554 577 588 704 655 452 590 834 547 524 562 1043 1043 1043 1043 319 319 373 373 642 804 802 796 762 832 762 740 794 767 275 331 780 470 780 472 458 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 419 412 445 948 948 468 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 487 735 ] endobj 470 0 obj <> endobj 471 0 obj <>stream %!PS-AdobeFont-1.1: RMTMI 1.1 %%CreationDate: 1993 May 10 16:52:31 % Copyright (c) 1992, 1993 The TeXplorators Corporation % Hinting Copyright (c) 1992, 1993 Y&Y, Inc. % MathTime is a trademark of The TeXplorators Corporation 11 dict begin /FontInfo 9 dict dup begin /version (1.1) readonly def /Notice (Copyright (C) 1992, 1993 The TeXplorators Corporation. Hinting (c) 1992, 1993 Y&Y, Inc. (508) 371-3286. All Rights Reserved.) readonly def /FullName (RMTMI) readonly def /FamilyName (MathTime) readonly def /Weight (Medium) readonly def /ItalicAngle -14.036 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /FontName /KQKGRM+RMTMI def /PaintType 0 def /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0] readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 0 /Gamma put dup 11 /alpha put dup 12 /beta put dup 59 /comma put dup 62 /greater put dup 46 /parenleft put dup 47 /parenright put dup 58 /period put dup 25 /pi put dup 27 /sigma put dup 61 /slash put dup 118 /v put dup 119 /w put readonly def /FontBBox{0 -213 987 680}readonly def currentdict end currentfile eexec oc;j~EЪ+`U+1;[ihHlgtR@nk{#Y~gJ[. DI~ْ+%hapYz;3NO_O:Vп}KBhIϮԬ";eiwzVcW;I0a1]j"4[{ErGT1QeG0 Vw ߚOҎN'·4b>T(4^mѨnV8Bo8cpWTC 6j'-б^3;ZSd_ v9(+2Op?.BXsޝo!.Y([J$~8g@/Y.Y+S$C9S= iYRu |íPq.`1)KB/к!xYJK8,2(ŝ]#BEQw5,Ge2u fPQ6PnhH~l 棉l|6Ҿj;D鿂 "zGN8fYC8#SfMr =XZ2MIHv@}`6)ta}Y7Ϳ47_75Ww ^6u$; ӕcYfg_2ƨ4}ȱG}THl=YUX 3y-kHj7έD,3>w(=?vez#]2+P)pvt2kDrn}۠>r|QkcRõ[I+s k)r5$i!(=EN$^ɼ}Yatw^ ם %Lbz{;%G{j7H9;S(Y_rGE.; _SW1@4'S$Gdp&? )cؔ%|M)1^&Ty Q|ea?Lfͅg'-u ]Q"x.W?(.;Կ'4$:??.O);AJvGr`iDS0N56>q5[8lv?Q7Ygo}Jط&ٶE;&d2z‡AFBQWki ',q;&sI-oi9%^eLDhLþLHU*I(N, PAD]vXIJ0+F=mWg5r& RXg|@,.ߤӖ|b>Cߠ+ewv*̄%^H ߞ>l-\4IBo $TkxKP %k,ffF^ qV; 6N)aQeB/% V,ϡ>aKDXo4tf,?Osm!f[|X.OUfBL&Ϥ3^PCn6N7J=jMXZu@Oa@V ):jvRh0"B`SxrDUD" F̋Wƌ>?R&#9X_żSPr2{sڲ{TA|FkMev[&?#.^m-X 8cT(Ixc?젡onkj.桟mpAW0ûV$4mu|35v^$K6y0 <|L#f^13%^ݠ =)@VfE;VqXÄ< j)tH3׾jT54AW3NR1U%߽I1L7LHi U+F5V3nj|\yfoVD'Z 0>?_|{Kv5 pJ*d\ɼ?T~2+oOH71Wi V*ӑO*ud~l r_O bT-.:eDc~nu}ρѹhH&ecii+(\XN{%LZKs$`"6~1ɜe;aS`W%QiC>_RtN/.D=TO G#ZhPPcINS$3<҂ P㦬F=(kH:և0FN c/݊+$;Bƒd2ڷ|8p1sEp-?=r B/!UedHР=%ocg4=3䌽b8,ݡ\xy亃<-tҨd-0{$hӓ v*/vƊ4gv΋XsLe$"M[g?b1Yz<x`UqxVCP 뀞!FY{p݁jS$ZEv#) 7-3~ͺ_i$oIBaN56}-t"z=F!q#9-㷀ȒgQ#uQx0 Ē_}h@*[TX6S}ڈ.63g@^ -pH0;j!BFt]ϋ6 Q=G,س@(ArfL ]CJc~"X!IIjF^*gߑn"_3`qodW>eW q,h|_2(1W-z*L #cð=fz _hMaR~F [ 5rO)4MfpUA+_,U^Pt"efgr*P-rE{~;UpwԝJ`K.I^>NQg>ar5|42[KK:s/[aӋHQ$f7K*&O >o`:^飼ƑPX"#zIHJFr26J0OVnPV[iendstream endobj 472 0 obj <> endobj 473 0 obj [ 278 278 556 556 556 556 556 556 556 556 556 556 278 278 584 584 584 500 1015 722 667 667 722 611 556 778 722 278 556 667 556 944 778 778 611 778 667 667 611 778 667 1000 722 667 611 333 278 333 584 500 278 556 611 500 611 556 333 611 611 278 278 500 278 944 611 611 611 611 389 500 333 611 556 833 ] endobj 474 0 obj <> endobj 475 0 obj <>stream %!PS-AdobeFont-1.0: t1-uni-regular 002.000 %%Title: t1-uni-regular %Version: 002.000 %%CreationDate: Sat Apr 12 22:19:08 2008 %%Creator: CV Radhakrishnan,,, %Copyright: Copyright (c) 1987, 1991, 1993, 1994, 1998 Adobe Systems %Copyright: Incorporated. All Rights Reserved.Univers is a trademark %Copyright: of Linotype-Hell AG and/or its subsidiaries. % Generated by FontForge 20070607 (http://fontforge.sf.net/) %%EndComments FontDirectory/t1-uni-regular known{/t1-uni-regular findfont dup/UniqueID known{dup /UniqueID get 4172112 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 11 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /USCGMP+t1-uni-regular def /FontBBox {-168 -250 992 997 }readonly def /UniqueID 4172112 def /PaintType 0 def /FontInfo 9 dict dup begin /version (002.000) readonly def /Notice (Copyright \050c\051 1987, 1991, 1993, 1994, 1998 Adobe Systems Incorporated. All Rights Reserved.Univers is a trademark of Linotype-Hell AG and/or its subsidiaries.) readonly def /FullName (Univers 55 Roman) readonly def /FamilyName (Univers) readonly def /Weight (Regular) readonly def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -100 def /UnderlineThickness 50 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 67 /C put dup 68 /D put dup 83 /S put dup 97 /a put dup 98 /b put dup 99 /c put dup 58 /colon put dup 101 /e put dup 103 /g put dup 104 /h put dup 105 /i put dup 106 /j put dup 108 /l put dup 109 /m put dup 110 /n put dup 111 /o put dup 112 /p put dup 46 /period put dup 114 /r put dup 115 /s put dup 47 /slash put dup 116 /t put dup 117 /u put dup 118 /v put dup 119 /w put readonly def currentdict end currentfile eexec oc;jAw-ᾉYň5t&נ{hLGqB`d˗Pة|*x\ޖHtEB-gedog7Q`[['W73sZ9 m !tAY!$tY\r[uTIUiBy[Ȝŗ3Kï6zJ!˒Js&B5CV]_I50$zEL>6µ3-O"Ղ,vw ;q8Q^Epd4_PsxO^2|jp5Ժ *Vg/ T"rɵ8t~k W%3M?$ۛWuGt5o6.2|#ԧ@ rد|C1k}')˃Umt8;:?2>GSQs2 KJۋaq%3(jv'T#o映ӲXƴpi-=@ؚi YCuC 纞 Wj/: IqyMG?rKiߣg d@rQKѴ:,] n0a]b g6ˈ}R2,^3>J TŘXbM]&Q2U}o=!X3Sq m0_׬P!C IKV.]!Nu}&QR0NtX.2_%R/d^4^˞Oqq+Q c,ީ)|.'ȣ_Ȁ`( H;1A CF=V˅O׼ s' k܎W;>) aݳaXY7Z bݱϚقf/?8U7>p'p 2ÅHA"&xt՝cs-|2N}i鍜`U+2&cW\LG.51n{uD Q'qGSe9ޡ(!@m:)IΏ;ipU@>\DKCV${Kt \׫̒O̗Ӌ9 ӦL-??sp!/$OMQ':Εz)|Y<^J8\qa_\ތQ*g{@N HnHƌoE kF%'nH깻L}j~RL^lV@vOkc}-e r % ME-eKi7ӈO^+l%"s1ZZ[%)%b??ihogC!4ZuuNT!ؼUpD΅"#pQ]gCǨ}dڌ%=c^C : Tix5j[U?SSӓ]!?dN@pBn.X֚^[AOsDMqAA[ 7?Dv +rʈ7^BS R9M?^ݬ@Q8@b6X.)ՆbgݷDY i$3/̯\! 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Z Awpnmp ';p7yC2nnڪdwS6`<ڄ_੝gmˈhɸ Nhυgy=ߞ.9I gH=øY2l"99T;E^ UK rb$&Ƀ ~> 6>ixY`a`y&5Tyfa{TX5 k]FTrISa4 Zmwu??-TO<¶̲#. /=2{( cj=JP8B;W!FN49jSAC:]mU]_Hw,t&}lvSDޕٳRjouH=n{ )ْFX"1{{@ OzdDivrr+GXןAI:5H:)fr}:^fZ5.^՚r>}{~]F@E *k*~?E6Ȓ(䀐)yn9H\"bSg7o,2io` [`mbs]h,񖪹(H=;+׭2-2=.7HITsshfIPb[q}Kf;57;_k)|^Ru{g&vfֺ+ ׎!]!k߉SQum$XEMp@Sf@O/$C`l=>amvFw~p!@i`ـ ԏ g_)j8ߛuNjm#B3~֊ȑM H%jT2 YAPo[@kq9V1m켭pnTw?2QZ*7ܔxg 2]酶 Yt@RpG֥5Mn2Ϙel%| F›B^,D~bXc'tlW=r4d7&Q ˾zR! |~`z$ 3=,T>^/6Z1 %}HKGr G2971ĽBMO~X{=dWe$ ye6p6M@ |qKM\2(P Q#'ĥ_-S{<萦.ZE&Ӝۣ#spď`dW#CM{#,gcH{%MM[RLX_ {ИN!o(12֮2ʕGIW<,zhO[3a7:Gݍ[G{RzJx{ r o\%[T!\^-%/R.ytӘD2}/H%{`WmZ[^L+̩3Y#'$V0m@ђR;]0sʓ`ikЇh _ޒIũՁ}"i2ۚ y\YcnKuaI%|>'_I;OIĂN<x+b{bFf g%,nQnAd:F>ZnRy׏ٜW ;)5"&Di;6Tqzisυjmg2|EG; KycHxpaՅLoZШ`l !?S@~n^t͍vP++jsX[3irļauOf@ (a ԋyKdi* x2|k:N]k8R3 ͏h~G.:ȟ* (w$_!Uwp15t53hcuHv6\ߛj2B~;zcRեIG {'l{& .|HL:Ϳ%FGmJ*5ln0dosRӫbs;iӎ)A0JC[.KX盽-4dEC+lM4aT@l БK5ir{fI|QA[lYS\4Rvxmƥru=ͅ3vPG#뼂^nӉMN[$Ifu;L)1==`q@Fq/!̜QU|E@ѿ'%YR]''"E)rT*\L0yeϊXގG`T0MKkh8esG(|+ebƛt>u+]9ٻ92G5}v J3U_%.YyLF˼fn;qgc儩xt־|۲C lD/R&ٞ!~&|(|M;E8A`J9@em^+i*{0ׯjcǸ8@kx6zcRեIG {$'pLa$+Kб4$˪-xr/V]򩩐-8{2LQ`7G0H5|iJ oͮ ;tT&TE;? 2ҁ_ie.)poϐԥɄo+S{ Yd}[w> =0,?&,H? +Bf% x+2Z <4礐ƒψcH3/U,9S@ondML-Ydr P+KOagU!`&Pc0L5%)պc0X:ў%m0`x{1]HzSZDJ*|9isJנ69W;#8@ ^E~yU3M7`XUbԆSbρzPxQgk]amN1E%4]O<1[޶z\pT:UKb@@-қTU"]}x XqQZ'~ (bmݫ/2T -%\O/D:($2&IC)4[+zF*SSctטtj56Q ai\/#ѯm֯X0϶t07Rv,#HLq 2 TnM#] ONI7j}0n#5n>@-Ki{ݚ@S:(^[t ꕹFMia}lrj5:0O/L>6i9*2hb7g2vx#WjR=3l#̈Tz9-[N|tamb*ZKZUkL}%Gl䩀y'TԚ.&* VeÔ 71]<3)etIOQz|ޗ˭JU=ooxj Հjiy eNa62a2h9 9 Pt`2<#^mF̶a%$s1*ތ= (sD 윗I(dگ´ln!NJy~JYM&n%秇j"cbkM'-3;tpJ}={_EXbgR )*e7`hPVg 43CѲf*ZpR!'2`J瓬v\wFI neL ,A}iC>@qK.%Us=ARQ^7 m'9'jJ F>lm]e֭[rvRfJIDXMs2y ٌ'M{v2oN^)Ri@kg4ɕ5<(느|ŜfU„/\n;d@YRDR-'pZÆ+wmyc>ںObx${`)Ж ]I:RbxcCJ=ZgB'֔qFOD]0\n[\K(Mu _yO"kt̝])HX4I^(1=6QaH:1[F˼3("ȿ6z>x<K|8$>7s.i?uC, \[ۧFX5mȦ_1?RM4MHK7,c.DNԝ1rbM0|q%cI ^G G"ۜ4N (ϝy;iQ[h!9sۃ*neazXm H+d;Y!)\"^*!rUpzO1ܳ8bO`/ zQ\ޥ3xVc PʾC~LČ&j2MEt3bdxs89QӃen(<۪۠a5.wn TbXA;Q?ȋ>g|8'g0~?Jg@!ganRϝUΧ"tcQ D*d/!"W%>Ux&L82j 12#y*i`.RKzY/zFow"t.\N:\&=sDw}r:=j#LD`~؟?BB(Fd@B#Av.<62%S݇:] # /@J<|P=7 l:&J)b2+ -zN ꀑ6^OCtʔQ\Y*ȴ;Jcrnn(l)iW#q_ 7-I`+T0 cEa- 6g:^2 ^AuR6M ʷNES˖VD\KǥK/Y#O .$Qm{ZGC7F?tSj\XA:BrkY!HX@ ~Qt}/=W p5뤅FKCSٵwIT胊 RU+^o8yG nMU[G>#"lc`]z*lny[\?$~wX{uK1>Aဴ$vtaaRbMk3l+O7ĠCƏpM: 6Bm͈L~u##V !@Cus8ht&Rej1CӅHrl`Ŀ,w6i+'> Dë;?f >uxBO7 }pmL܉rݨ9;k0)ks3_3Ȁe)Mf2Qf1EѸ!lÜs12ov!;0*Gʎ}mڐ/{#;ݩZQM6!6lK!@Mx~303 p~t?,+\_F7NkӲ_Ts<*,xz0s䒤qe-9"B p[ӕ!#F'8`(xa :_7'͟1E7[&(˭_qh$$k2 @e,a.l.wQ]'Epm  z`NB!//k?׭`wόť.l> endobj 477 0 obj [ 579 820 0 931 286 289 600 572 565 861 854 1000 405 413 685 490 565 768 227 373 377 401 549 227 408 229 313 553 553 553 553 553 553 553 553 553 553 316 316 549 549 549 504 779 607 575 577 694 539 486 658 715 301 297 616 474 890 700 682 539 682 587 490 518 687 609 981 605 569 528 343 352 343 549 500 217 533 543 450 556 480 300 514 564 286 289 520 274 864 578 533 556 537 397 408 354 578 517 806 491 524 448 ] endobj 478 0 obj <> endobj 479 0 obj <>stream %!PS-AdobeFont-1.0: t1-gul-regular-italic 001.001 %%Title: t1-gul-regular-italic %Version: 001.001 %%CreationDate: Mon May 26 10:31:00 2008 %%Creator: CV Radhakrishnan,,, %Copyright: Gulliver, Giant amongst Dwarfs. %Copyright: This typeface offers excellent readability at very small %Copyright: sizes. %Copyright: %Copyright: The digitally encoded machine readable outline data for %Copyright: producing the typefaces licensed to you is copyrighted (c), %Copyright: 1994, 2005 by and the property of Gerard Unger. % Generated by FontForge 20070607 (http://fontforge.sf.net/) %%EndComments FontDirectory/t1-gul-regular-italic known{/t1-gul-regular-italic findfont dup/UniqueID known{dup /UniqueID get 4109950 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 12 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /LITVCG+t1-gul-regular-italic def /FontBBox {-141 -321 1053 1055 }readonly def /UniqueID 4109950 def /XUID [1021 938 1479029120 1353546] def /PaintType 0 def /FontInfo 11 dict dup begin /version (001.001) readonly def /Notice (Gulliver, Giant amongst Dwarfs.\012This typeface offers excellent readability at very small sizes.\012\012The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted \050c\051, 1994, 2005 by and the property of Gerard Unger.) readonly def % Gulliver, Giant amongst Dwarfs. % This typeface offers excellent readability at very small sizes. % % The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted (c), 1994, 2005 by and the property of Gerard Unger. /FullName (Gulliver Italic) readonly def /FamilyName (Gulliver) readonly def /Weight (Regular) readonly def /FSType 4 def /ItalicAngle -8.5 def /isFixedPitch false def /UnderlinePosition -75 def /UnderlineThickness 50 def /ascent 789 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 66 /B put dup 67 /C put dup 68 /D put 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M)2p,TL]g ;uvN;&KBYy3n -!$h/FT)Y,qZVZ֑/v.G~N#8ƍOZ]lЅSOgP!\q!Gn!ힹa:2u8rY$WL 7#TMӚ{ٽde`ci#=?f5Έ54kJDND Zvm^*d[@1 *n:l#=sx[ZE7Ă[{Wk"#ѝ[tPi.2Z&£Keng yw%3x[ *Q5AS-98 0)5MּRu'O.3gǨ2Tksf3K+mi6|re^#S58kXKj(ZHl/U4XrK)*ݔ4/+~ʔ4,ߖ= ,~?P):'QwU&ͧGܭ`gȭL}HV0>VQ.b+< ȳG2]QG$ ꔩW*ȹUAsv%Uun'  `La97p=xp[z? tݳJk tA>{?-T˙xyKpNVqinjd1k~Ikc4mqK es~%AIMT\ KpN$תB,~ɫ:6u4Ф JV")Yqmy+g  yuѝ=k\9UʚXsDգpB{fCm-u$WPܙݻ'ݶ\g*/ kNp,k|&X5(e'VlBADųq3d1+nH6v_n E<Ι%#2 !n4 Ďv"^%2v^xrV~{q:)U*qܲC`.`rwAu'VP1T=@$QJC'5zbu$|& U-~B+љ na5%*ۀivJz˘ (`&ν S`ٌ_)'`ӿF!e"=ez-v%BMIj)J9eCdơ'$@9Y΍Yk.m~::ܚ^VM0-Ļ3߈{|"gR_}d@>ƒ;L01D_sPWAmUS) [j?=?;AfVޱWWFܮs\R=_ y0IM}_˾NSq8.sw wcWؖc!;YE*-Eh9 KTiEW;b%?ӭF?gb;Od2v<΀7~zќ\1 {r=?>̰=IOW¹!4O5/a z^K_}j`_/foPOaUUL 4qׅ xsV#(<(l"%DV w2k&@azT9cI6 ԁIxlnYwP0l,[BH8%/Z0Roy'56Rקa q}endstream endobj 480 0 obj <> endobj 481 0 obj [ 256 289 582 582 582 582 582 582 582 582 582 582 310 310 549 549 549 533 872 672 638 604 726 602 551 671 756 346 337 705 535 936 736 730 627 730 662 528 572 728 675 1040 701 635 598 381 385 381 549 500 251 548 611 499 622 541 378 566 651 326 324 627 325 979 653 605 618 610 452 458 398 644 547 862 562 ] endobj 482 0 obj <> endobj 483 0 obj <>stream %!PS-AdobeFont-1.0: t1-gul-bold 001.001 %%Title: t1-gul-bold %Version: 001.001 %%CreationDate: Mon May 26 10:32:29 2008 %%Creator: CV Radhakrishnan,,, %Copyright: Gulliver, Giant amongst Dwarfs. %Copyright: This typeface offers excellent readability at very small %Copyright: sizes. %Copyright: %Copyright: The digitally encoded machine readable outline data for %Copyright: producing the typefaces licensed to you is copyrighted (c), %Copyright: 1994, 2005 by and the property of Gerard Unger. % Generated by FontForge 20070607 (http://fontforge.sf.net/) %%EndComments FontDirectory/t1-gul-bold known{/t1-gul-bold findfont dup/UniqueID known{dup /UniqueID get 4090458 eq exch/FontType get 1 eq and}{pop false}ifelse {save true}{false}ifelse}{false}ifelse 12 dict begin /FontType 1 def /FontMatrix [0.001 0 0 0.001 0 0 ]readonly def /FontName /CWBEZM+t1-gul-bold def /FontBBox {-150 -371 1131 1082 }readonly def /UniqueID 4090458 def /XUID [1021 992 867865856 10469850] def /PaintType 0 def /FontInfo 11 dict dup begin /version (001.001) readonly def /Notice (Gulliver, Giant amongst Dwarfs.\012This typeface offers excellent readability at very small sizes.\012\012The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted \050c\051, 1994, 2005 by and the property of Gerard Unger.) readonly def % Gulliver, Giant amongst Dwarfs. % This typeface offers excellent readability at very small sizes. % % The digitally encoded machine readable outline data for producing the typefaces licensed to you is copyrighted (c), 1994, 2005 by and the property of Gerard Unger. /FullName (Gulliver Bold) readonly def /FamilyName (Gulliver) readonly def /Weight (Bold) readonly def /FSType 4 def /ItalicAngle 0 def /isFixedPitch false def /UnderlinePosition -75 def /UnderlineThickness 50 def /ascent 789 def end readonly def /Encoding 256 array 0 1 255 {1 index exch /.notdef put} for dup 65 /A put dup 69 /E put dup 70 /F put dup 80 /P put dup 82 /R put dup 84 /T put dup 97 /a put dup 98 /b put dup 99 /c put dup 100 /d put dup 101 /e put dup 56 /eight put dup 102 /f put dup 53 /five put dup 52 /four put dup 103 /g put dup 104 /h put dup 105 /i put dup 107 /k put dup 108 /l put dup 109 /m put dup 110 /n put dup 57 /nine put dup 111 /o put dup 49 /one put dup 46 /period put dup 114 /r put dup 115 /s put dup 55 /seven put dup 54 /six put dup 116 /t put dup 51 /three put dup 50 /two put dup 117 /u put dup 118 /v put dup 119 /w put dup 120 /x put dup 48 /zero put readonly def currentdict end currentfile eexec oc;jAw-<X2-Τ^tE_SKF1F^jNBq{y4-Fgbԓ{"WB:rP ?dgS%|'ؓw&F7JNL9VRtbT5'm\N"K< wJv$tE;D4Vܢv{oߩ?@(L[ov#0z[mW9GU@$ilLѨ8Mp!29"u]XoM^ R`@KP Ѩ9c~VA-۩+-3G?ZvrKۈsy7.iXU#;߳Wį H~zVbh'u]wP^I-?6\T"K7& n-ku9yD#`itϳPjǺs8r\B^ݼ 'nMPskm`TWF}]:4iX 뿉N^fR,qGظ֠yNx^r@])z܆L{9[U‡n9ơf9Wn"'X͘1#d E+3Ll\.S~ٛ_7ߴ1 N4.I#'f˖7ݩKi0L768 T5l3>HBpPxeU] 񀆊,^ S6]v>J~iY XWgzK$'Q-긇H!V܁d!;d4T5:,v#cK*;+zXz k =Yu6[T_}Mi}p~.<#8ϵew]1~W/dTD6N?P`0 &q+]<4[~Uу0G6m#^x#\Ǽ:X)/='KWXW37tJe pɦϐrߙ|j,4^"JCZQyvf7\ /O˫\Q,ļcE7]PA+<>7y:,,E{:}1\\6W% Ђ ӥGy{cdܠ2?&\"{HUc ġVLԅrl5 92h羦`x@m}{$H')\Q%"*G9=S._y!P>F~,w*5i1m@S,GV3~K̳'Ҁ&gK@6) .r8kV)X';! 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[R#Eq.&Hqu9s.[]峚*m-EUF L\Axeh}8mǖ@e{`~4U(m3 z)ؑ>&}8f{ZTw~~1i9v8t(ö9XҔg`T D.m\NÞs9D [0`7C$IfnM}@Pn7_lZP x w/)@iF&*ӮNƟUOH 0ɩNL.l"Jg2R Mt&DAރ YDJRJ|QK]A8DAA-Wba,M,x?2{ "V1ԂP}?ax`ģ%kbʴ$/贮0( rݰ;Po'ǿ~W;pF3Efmv좑Da@;KЛы{5 ~Ebj;[jJ,fԹ[['ay ƀ-d&^M1y:K's.[*\.9[6BT`JGL7EѣPqrx0ίWPF`aaö o֗qMpAls襣 }xA b[PC(>RbTFQ"s 3Tz(nZg ܁:IlCju whMŅSP{[Cy"ōZ`|+n$"'7@ߘ*V_,o&5`z%QMRd Mð{u&`Ct:+z/ו:AsAsx>9@DTF8U܊ߞF4oCeJoV{)Yؓ?bhϸ\N$O>FxQ~{91fkٝ2 Us_rqucX˰)tCsWLvk!Cء042٬,DSa}DZ!A lŲHrNzEMz3ZS֐x]ȹ-ZǺ۬$OQ5A߁= 0z-!ަD#wD0Y h:޳~os|f:FD OV3F頄V4>jՅU\Ɂ8 p\Dlp MBP?/ } $y({})eza=S!SifWa+꠼ %2qI:ɔř,6}E A"Hf=9>D B9i8m)0+(T/ۘp,ؼjx7&XB *6L<{U1 U1V s}OgC$X xrCq=-Ҳjxa&mtvC=n0xpz|Oa\XwIkoƛ+hgojPY Ĭ h}vW>i{!{xo)&W *$6 RNV.F`z,0F5%b7U;޽`]߈Iљ=ȌP!%Vɏ- a6}9Ҝ~T]cTySlQpUfmIɘ'XM @g{n 7yHOOfP\ZDVNM qПAkAx"$nˑ$bN#L,G=f4_WRi%BnK臼!]L}`xW5B!Zj$g) 礚5ԝZGOuI,rL; $ G<;|p?1j d F]H ,Ilӊ4ۙ}/1;5">ļ4|X9ZxNqlŻ%5>u8FjiE!%Gt(]٪YG`anmFdLn{J_7̿CA.(>BU$e^=5ږogN}$u7ozK{tx4C${wSBX:Lj`hJ:๎biq7$PUb]_*dߐ1i{)Di Ciu• 7lF"_gJ:Zv ctk 4vLjq9DoY-"2悪gz(AԳtfz0-wx‚9vÌœG sqB#f>y§no)RDQO _óYniK[CFM/"xQrod$t̖!I{̧uZxU6΁#yʆδ&5go}FLVHU+91@v$TH~ 6uS ख़B[{?xILT1E:z]VF7>1<[1&NQ}m nJ5H-!&<)6#W5kɔ> endobj 485 0 obj [ 780 278 784 521 780 556 780 780 800 800 800 800 800 1000 500 500 780 780 780 780 754 754 754 754 780 780 780 780 984 984 754 754 1099 1099 616 616 1043 985 985 780 1043 1043 704 704 1043 985 985 762 270 1021 629 629 784 784 1 1 556 519 722 556 733 635 780 780 634 425 452 780 780 451 536 536 780 357 333 333 333 333 333 333 333 333 347 728 333 333 275 277 700 776 776 668 668 668 700 700 662 662 444 444 444 444 370 370 367 367 286 498 616 711 485 ] endobj 486 0 obj <> endobj 487 0 obj <>stream %!PS-AdobeFont-1.1: MTSYN 1.000 %%CreationDate: 1996 Aug 26 20:27:17 % Copyright (c) 1996 Michael Spivak. % Hinting Copyright (c) 1996 Y&Y, Inc. 11 dict begin /FontInfo 9 dict dup begin /version (1.000) readonly def /Notice (Copyright (c) 1992-1996 Michael Spivak. 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[(representations)-236(and)-236(pictures.)-236(Such)-236(explicit)-236(representations)-236(can)-236(also)-235(in)-236(principle)-236(be)-236(used)-236(to)-236(clarify)-236(the)]TJ ET 1 0 0 1 39.797 505.452 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -505.452 cm BT /F51 8.2889 Tf 39.797 494.991 Td [(calculation)-208(and)-209(understanding)-208(of)-208(abstract)-209(invariants)-208(of)-209(the)-208(manifolds.)-209(Among)-208(the)-208(classes)-209(of)-208(geometric)]TJ ET 1 0 0 1 39.797 494.991 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -494.991 cm BT /F51 8.2889 Tf 39.797 484.531 Td [(objects)-458(that)-458(have)-458(a)-459(long)-458(history)-458(of)-458(interest)-458(are)-458(the)-458(algebraic)-459(varieties)-458(defined)-458(by)-458(homogeneous)]TJ ET 1 0 0 1 39.797 484.531 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -484.531 cm BT /F51 8.2889 Tf 39.797 474.07 Td [(polynomials)-379(in)-379(complex)-379(projective)-379(spaces.)-379(One)-379(such)-379(family,)-379(the)-379(algebraic)-379(curves)-379(in)]TJ/F144 8.6077 Tf 328.9 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 6.998 -3.472 Td [(\050see,)-379(e.g.,)]TJ ET 1 0 0 1 39.797 474.07 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.461 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -39.797 -463.609 cm BT /F51 8.2889 Tf 39.797 463.609 Td [(Hanson)]TJ ET 1 0 0 1 68.717 463.609 cm 0 g 0 G 1 0 0 1 -68.717 -463.609 cm BT /F51 8.2889 Tf 71.919 463.609 Td [(\050)]TJ ET 1 0 0 1 74.986 463.609 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -74.986 -463.609 cm BT /F51 8.2889 Tf 74.986 463.609 Td [(1994)]TJ ET 1 0 0 1 94.183 463.609 cm 0 g 0 G 1 0 0 1 -94.183 -463.609 cm BT /F51 8.2889 Tf 94.183 463.609 Td [(\051\051,)-387(has)-386(recently)-386(served)-387(the)-386(purpose)-386(of)-387(providing)-386(explicit)-387(images)-386(of)-386(cross-sections)-387(of)]TJ ET 1 0 0 1 39.797 463.609 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -463.609 cm BT /F51 8.2889 Tf 39.797 453.148 Td [(Calabi\025Yau)-297(spaces,)-297(and)-297(has)-297(been)-297(used)-297(to)-298(represent)-297(the)-297(hidden)-297(dimensions)-297(of)-297(string)-297(theory)-297(\050)]TJ ET 1 0 0 1 393.086 453.148 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -393.086 -453.148 cm BT /F51 8.2889 Tf 393.086 453.148 Td [(Greene)]TJ ET 1 0 0 1 420.423 453.148 cm 0 g 0 G 1 0 0 1 -420.423 -453.148 cm BT /F51 8.2889 Tf 420.423 453.148 Td [(,)]TJ ET 1 0 0 1 39.797 453.148 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.46 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -39.797 -442.688 cm BT /F51 8.2889 Tf 39.797 442.688 Td [(1999)]TJ ET 1 0 0 1 58.994 442.688 cm 0 g 0 G 1 0 0 1 -58.994 -442.688 cm BT /F51 8.2889 Tf 58.994 442.688 Td [(\051,)-496(for)-496(which)-496(very)-496(few)-496(other)-496(methods)-495(of)-496(producing)-496(images)-496(are)-496(available.)-497(While)-496(one)-496(might)]TJ ET 1 0 0 1 39.797 442.688 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -442.688 cm BT /F51 8.2889 Tf 39.797 432.227 Td [(have)-351(guessed)-352(that)-351(the)-352(methods)-351(used)-352(for)]TJ/F144 8.6077 Tf 159.372 0 Td [(C)]TJ/F108 8.2889 Tf 6.216 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 6.771 -3.472 Td [(could)-351(be)-352(extended)-351(trivially)-352(to)]TJ/F144 8.6077 Tf 117.986 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(3)]TJ/F51 8.2889 Tf 6.771 -3.472 Td [(and)-351(other)-352(higher-)]TJ ET 1 0 0 1 39.797 432.227 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -432.227 cm BT /F51 8.2889 Tf 39.797 421.766 Td [(dimensional)-250(projective)-250(spaces,)-250(the)-250(problem)-250(turns)-250(out)-250(to)-250(be)-250(fairly)-250(complex.)]TJ ET 1 0 0 1 39.797 421.766 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -421.766 cm BT /F51 8.2889 Tf 51.752 411.391 Td [(Let)-250(us)-250(now)-250(be)-250(more)-250(precise.)-250(We)-250(will)-250(show)-250(the)-250(following:)]TJ ET 1 0 0 1 39.797 411.391 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -14.842 cm 0 g 0 G 1 0 0 1 -35.812 -396.549 cm BT /F108 8.2889 Tf 39.797 396.549 Td [(Theorem.)]TJ ET 1 0 0 1 77.901 396.549 cm 0 g 0 G 1 0 0 1 -77.901 -396.549 cm BT /F52 8.2889 Tf 81.886 396.549 Td [(For)-408(any)-407(given)-408(positive)-408(integer)-408(n,)-408(there)-407(is)-408(a)-408(tessellation)-408(on)-407(F)]TJ/F52 5.8022 Tf 226.174 -1.435 Td [(n)]TJ/F52 8.2889 Tf 7.232 1.435 Td [(with)]TJ/F51 8.2889 Tf 20.04 0 Td [(6)]TJ/F52 8.2889 Tf 4.8 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.471 Td [(3)]TJ/F51 8.2889 Tf 7.237 -3.471 Td [(4)]TJ/F52 8.2889 Tf 4.799 0 Td [(-cells.)-409(Each)]TJ/F51 8.2889 Tf 44.971 0 Td [(4)]TJ/F52 8.2889 Tf 4.799 0 Td [(-cell)]TJ ET 1 0 0 1 39.797 396.549 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -396.549 cm BT /F52 8.2889 Tf 39.797 386.088 Td [(is)-354(bounded)-353(by)-354(four)-354(pentahedrons.)-354(Each)-354(pentahedron)-353(is)-354(a)-354(pyramid)-354(with)-353(one)-354(quadrilateral)-354(face)-353(and)-354(four)]TJ ET 1 0 0 1 39.797 386.088 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -386.088 cm BT /F52 8.2889 Tf 39.797 375.627 Td [(triangular)-436(faces.)-437(The)-436(tessellation)-436(is)-436(invariant)-436(under)-436(the)-436(action)-436(of)-436(the)-436(group)]TJ/F192 9.2055 Tf 289.174 0 Td [(\000)]TJ/F52 5.8022 Tf 5.725 -1.434 Td [(n)]TJ/F52 8.2889 Tf 3.852 1.434 Td [(,)-436(where)]TJ/F192 9.2055 Tf 31.715 0 Td [(\000)]TJ/F52 5.8022 Tf 5.726 -1.434 Td [(n)]TJ/F52 8.2889 Tf 7.465 1.434 Td [(consists)-436(of)]TJ ET 1 0 0 1 39.797 375.627 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -375.627 cm BT /F52 8.2889 Tf 39.797 365.166 Td [(isomorphisms)-212(of)-211(F)]TJ/F52 5.8022 Tf 65.06 -1.434 Td [(n)]TJ/F52 8.2889 Tf 5.605 1.434 Td [(induced)-212(from)-211(permutations)-212(and)-211(phase)-212(multiplications)-211(of)-212(the)-211(homogeneous)-212(coordinates)]TJ ET 1 0 0 1 39.797 365.166 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -365.166 cm BT /F52 8.2889 Tf 39.797 354.706 Td [(of)]TJ/F144 8.6077 Tf 8.977 0 Td [(C)]TJ/F108 8.2889 Tf 6.216 0 Td [(P)]TJ/F51 5.8022 Tf 5.198 3.471 Td [(3)]TJ/F52 8.2889 Tf 3.857 -3.471 Td [(.)-250(The)-250(group)]TJ/F192 9.2055 Tf 42.431 0 Td [(\000)]TJ/F52 5.8022 Tf 5.725 -1.435 Td [(n)]TJ/F52 8.2889 Tf 5.924 1.435 Td [(acts)-250(transitively)-250(on)-250(the)-250(set)-250(of)]TJ/F51 8.2889 Tf 106.263 0 Td [(4)]TJ/F52 8.2889 Tf 4.8 0 Td [(-cells)-250(of)-250(the)-250(tessellation.)]TJ ET 1 0 0 1 39.797 354.706 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -354.706 cm BT /F51 8.2889 Tf 51.752 339.778 Td [(Altogether,)-276(the)-277(tessellation)-276(has)-277(6)]TJ/F52 8.2889 Tf 125.616 0 Td [(n)]TJ/F51 8.2889 Tf 7.082 0 Td [(vertices,)-276(12)]TJ/F52 8.2889 Tf 43.686 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F51 8.2889 Tf 6.149 -3.472 Td [(edges,)-276(8)]TJ/F52 8.2889 Tf 30.871 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F191 9.5641 Tf 6.208 -3.472 Td [(C)]TJ/F51 8.2889 Tf 9.81 0 Td [(7)]TJ/F52 8.2889 Tf 4.799 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(3)]TJ/F51 8.2889 Tf 6.149 -3.472 Td [(2-cells)-276(\0503)]TJ/F52 8.2889 Tf 35.347 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(3)]TJ/F51 8.2889 Tf 6.149 -3.472 Td [(quadrilaterals)-276(and)]TJ ET 1 0 0 1 39.797 339.778 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -339.778 cm BT /F51 8.2889 Tf 39.797 329.317 Td [(8)]TJ/F52 8.2889 Tf 4.799 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F191 9.5641 Tf 4.381 -3.472 Td [(C)]TJ/F51 8.2889 Tf 7.984 0 Td [(4)]TJ/F52 8.2889 Tf 4.799 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(3)]TJ/F51 8.2889 Tf 5.409 -3.472 Td [(triangles\051,)-187(12)]TJ/F52 8.2889 Tf 49.47 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(3)]TJ/F51 8.2889 Tf 5.409 -3.472 Td [(3-cells)-187(\050pyramids\051)-187(and)-188(6)]TJ/F52 8.2889 Tf 91.008 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(3)]TJ/F51 8.2889 Tf 5.409 -3.472 Td [(4-cells.)-188(It)-187(is)-187(known)-187(that)-187(the)-188(Euler)-187(characteristic)-187(of)]TJ ET 1 0 0 1 39.797 329.317 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -329.317 cm BT /F51 8.2889 Tf 39.797 318.856 Td [(any)-210(smooth)-211(algebraic)-210(surface)-211(of)-210(degree)]TJ/F52 8.2889 Tf 148.614 0 Td [(n)]TJ/F51 8.2889 Tf 6.535 0 Td [(in)]TJ/F144 8.6077 Tf 9.254 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(3)]TJ/F51 8.2889 Tf 5.602 -3.472 Td [(is)-210(6)]TJ/F52 8.2889 Tf 12.726 0 Td [(n)]TJ/F191 9.5641 Tf 5.907 0 Td [(\000)]TJ/F51 8.2889 Tf 8.576 0 Td [(4)]TJ/F52 8.2889 Tf 4.799 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F191 9.5641 Tf 4.973 -3.472 Td [(C)]TJ/F52 8.2889 Tf 8.576 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(3)]TJ/F51 8.2889 Tf 5.601 -3.472 Td [(\050see,)-211(e)1(.g.,)]TJ ET 1 0 0 1 317.556 318.856 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -317.556 -318.856 cm BT /F51 8.2889 Tf 317.556 318.856 Td [(Griffiths)-210(and)-211(Harris)]TJ ET 1 0 0 1 390.289 318.856 cm 0 g 0 G 1 0 0 1 -390.289 -318.856 cm BT /F51 8.2889 Tf 392.033 318.856 Td [(\050)]TJ ET 1 0 0 1 395.1 318.856 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -395.1 -318.856 cm BT /F51 8.2889 Tf 395.1 318.856 Td [(1978)]TJ ET 1 0 0 1 414.297 318.856 cm 0 g 0 G 1 0 0 1 -414.297 -318.856 cm BT /F51 8.2889 Tf 414.297 318.856 Td [(\051\051.)]TJ ET 1 0 0 1 39.797 318.856 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -318.856 cm BT /F51 8.2889 Tf 39.797 308.396 Td [(One)-169(handily)-169(verifies)-169(from)-168(our)-169(tessellation)-169(for)]TJ/F52 8.2889 Tf 168.174 0 Td [(F)]TJ/F52 5.8022 Tf 4.028 -1.435 Td [(n)]TJ/F51 8.2889 Tf 5.252 1.435 Td [(that)-169(this)-169(is)-169(equal)-169(to)-168(6)]TJ/F52 8.2889 Tf 76.543 0 Td [(n)]TJ/F191 9.5641 Tf 4.847 0 Td [(\000)]TJ/F51 8.2889 Tf 7.517 0 Td [(12)]TJ/F52 8.2889 Tf 9.598 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.471 Td [(2)]TJ/F191 9.5641 Tf 3.914 -3.471 Td [(C)]TJ/F192 9.5641 Tf 7.517 0 Td [(.)]TJ/F51 8.2889 Tf 3.567 0 Td [(8)]TJ/F52 8.2889 Tf 4.8 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.471 Td [(2)]TJ/F191 9.5641 Tf 3.914 -3.471 Td [(C)]TJ/F51 8.2889 Tf 7.516 0 Td [(7)]TJ/F52 8.2889 Tf 4.8 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.471 Td [(3)]TJ/F192 9.5641 Tf 3.857 -3.471 Td [(/)]TJ/F191 9.5641 Tf 3.624 0 Td [(\000)]TJ/F51 8.2889 Tf 7.517 0 Td [(12)]TJ/F52 8.2889 Tf 9.598 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.471 Td [(3)]TJ/F191 9.5641 Tf 3.914 -3.471 Td [(C)]TJ/F51 8.2889 Tf 7.517 0 Td [(6)]TJ/F52 8.2889 Tf 4.799 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.471 Td [(3)]TJ/F51 8.2889 Tf 3.858 -3.471 Td [(,)]TJ ET 1 0 0 1 39.797 308.396 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -308.396 cm BT /F51 8.2889 Tf 39.797 297.935 Td [(i.e.,)-250(the)-250(alternating)-250(sum)-250(of)-250(the)-250(numbers)-250(of)-250(vertices,)-250(edges,)-250(2-cells,)-250(3-cells,)-250(and)-250(4-cells.)]TJ ET 1 0 0 1 39.797 297.935 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -297.935 cm BT /F51 8.2889 Tf 51.752 287.56 Td [(Notice)-355(that)-354(the)-355(restriction)-355(to)]TJ/F52 8.2889 Tf 114.887 0 Td [(F)]TJ/F52 5.8022 Tf 4.028 -1.435 Td [(n)]TJ/F51 8.2889 Tf 6.792 1.435 Td [(of)-355(the)-354(natural)-355(projection)]TJ/F144 8.6077 Tf 98.478 0 Td [(C)]TJ/F108 8.2889 Tf 6.216 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.471 Td [(3)]TJ/F191 9.5641 Tf 6.873 -3.471 Td [(n)-315(fT)]TJ/F51 8.2889 Tf 14.378 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(1)]TJ/F191 9.5641 Tf 4.8 0 Td [(Ug)-510(!)]TJ/F144 8.6077 Tf 26.997 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.471 Td [(2)]TJ/F51 8.2889 Tf 3.858 -3.471 Td [(,)-355(given)-354(by)]TJ ET 1 0 0 1 39.797 287.56 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -287.56 cm BT /F191 9.5641 Tf 39.797 277.099 Td [(T)]TJ/F52 8.2889 Tf 3.185 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(0)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.759 0 Td [(z)]TJ/F51 5.8022 Tf 3.714 -1.435 Td [(1)]TJ/F192 9.5641 Tf 3.857 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(2)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(3)]TJ/F191 9.5641 Tf 3.858 1.435 Td [(U)-278(7)1(!)-278(T)]TJ/F52 8.2889 Tf 22.194 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(0)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.759 0 Td [(z)]TJ/F51 5.8022 Tf 3.714 -1.435 Td [(1)]TJ/F192 9.5641 Tf 3.857 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(2)]TJ/F191 9.5641 Tf 3.858 1.435 Td [(U)]TJ/F51 8.2889 Tf 3.185 0 Td [(,)-250(is)-250(a)-250(regular)]TJ/F52 8.2889 Tf 48.108 0 Td [(n)]TJ/F51 8.2889 Tf 4.791 0 Td [(-fold)-250(branched)-250(covering)]TJ ET 1 0 0 1 39.797 277.099 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -14.842 cm 0 g 0 G 0 g 0 G 1 0 0 1 -35.812 -262.257 cm BT /F192 9.5641 Tf 63.707 262.257 Td [(\033)]TJ/F191 9.5641 Tf 9.007 0 Td [(V)]TJ/F52 8.2889 Tf 5.287 0 Td [(F)]TJ/F52 5.8022 Tf 4.029 -1.435 Td [(n)]TJ/F191 9.5641 Tf 6.508 1.435 Td [(!)]TJ/F144 8.6077 Tf 13.168 0 Td [(C)]TJ/F108 8.2889 Tf 6.216 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.95 Td [(2)]TJ ET 1 0 0 1 409.365 262.257 cm 0 g 0 G 1 0 0 1 -409.365 -262.257 cm BT /F51 8.2889 Tf 411.438 262.257 Td [(\0502\051)]TJ ET 1 0 0 1 422.362 262.257 cm 0 g 0 G 1 0 0 1 -382.565 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -262.257 cm BT /F51 8.2889 Tf 39.797 247.329 Td [(which)-250(is)-250(branched)-250(over)-250(the)-250(algebraic)-250(curve)-250(in)]TJ/F144 8.6077 Tf 174.894 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 5.93 -3.472 Td [(defined)-250(by)-250(the)-250(equation)]TJ ET 1 0 0 1 39.797 247.329 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -14.842 cm 0 g 0 G 0 g 0 G 1 0 0 1 -35.812 -232.487 cm BT /F52 8.2889 Tf 63.707 232.487 Td [(z)]TJ/F52 5.8022 Tf 5.381 3.95 Td [(n)]TJ/F51 5.8022 Tf -1.667 -6.523 Td [(0)]TJ/F191 9.5641 Tf 7.644 2.573 Td [(C)]TJ/F52 8.2889 Tf 9.585 0 Td [(z)]TJ/F52 5.8022 Tf 5.38 3.95 Td [(n)]TJ/F51 5.8022 Tf -1.667 -6.523 Td [(1)]TJ/F191 9.5641 Tf 7.644 2.573 Td [(C)]TJ/F52 8.2889 Tf 9.586 0 Td [(z)]TJ/F52 5.8022 Tf 5.38 3.95 Td [(n)]TJ/F51 5.8022 Tf -1.667 -6.523 Td [(2)]TJ/F191 9.5641 Tf 8.176 2.573 Td [(D)]TJ/F51 8.2889 Tf 10.116 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(:)]TJ ET 1 0 0 1 409.365 232.487 cm 0 g 0 G 1 0 0 1 -409.365 -232.487 cm BT /F51 8.2889 Tf 411.438 232.487 Td [(\0503\051)]TJ ET 1 0 0 1 422.362 232.487 cm 0 g 0 G 1 0 0 1 -382.565 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -232.487 cm BT /F51 8.2889 Tf 51.752 216.475 Td [(The)-283(tessellation)-282(of)]TJ/F52 8.2889 Tf 72.252 0 Td [(F)]TJ/F52 5.8022 Tf 4.028 -1.435 Td [(n)]TJ/F51 8.2889 Tf 6.194 1.435 Td [(we)-283(present)-282(is)-283(a)-282(lift)-283(from)]TJ/F192 9.5641 Tf 94.257 0 Td [(\033)]TJ/F51 8.2889 Tf 8.693 0 Td [(of)-283(a)-282(tessellation)-283(of)]TJ/F144 8.6077 Tf 72.339 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.471 Td [(2)]TJ/F51 8.2889 Tf 3.857 -3.471 Td [(,)-283(which)-282(is)-283(an)-282(extension)-283(of)]TJ ET 1 0 0 1 39.797 216.475 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -216.475 cm BT /F51 8.2889 Tf 39.797 206.014 Td [(a)-327(tessellation)-327(\050triangulation\051)-326(of)-327(the)-327(algebraic)-327(curve)]TJ ET 1 0 0 1 238.487 206.014 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -238.487 -206.014 cm BT /F51 8.2889 Tf 238.487 206.014 Td [(\050)]TJ ET 1 0 0 1 241.554 206.014 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -241.554 -206.014 cm BT /F51 8.2889 Tf 241.554 206.014 Td [(3)]TJ ET 1 0 0 1 246.353 206.014 cm 0 g 0 G 1 0 0 1 -246.353 -206.014 cm BT /F51 8.2889 Tf 246.353 206.014 Td [(\051.)-327(This)-327(approach)-327(greatly)-327(reduces)-327(the)-326(difficulty)]TJ ET 1 0 0 1 39.797 206.014 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -206.014 cm BT /F51 8.2889 Tf 39.797 195.553 Td [(caused)-362(by)-361(the)-362(topological)-362(complexity)-362(of)]TJ/F52 8.2889 Tf 158.719 0 Td [(F)]TJ/F52 5.8022 Tf 4.028 -1.435 Td [(n)]TJ/F51 8.2889 Tf 3.852 1.435 Td [(,)-362(as)-362(the)-361(geometry)-362(and)-362(topology)-362(of)]TJ/F144 8.6077 Tf 135.393 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td 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Tf 5.1 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(=)]TJ/F52 5.8022 Tf 7.833 0 Td [(n)]TJ/F191 9.5641 Tf 3.852 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.184 0 Td [(;)]TJ/F51 8.2889 Tf 13.049 0 Td [(0)]TJ/F191 9.5641 Tf 7.456 0 Td [(\024)]TJ/F52 8.2889 Tf 9.868 0 Td [(t)]TJ/F191 9.5641 Tf 6.299 0 Td [(\024)]TJ/F192 9.5641 Tf 11.064 6.705 Td [(\031)]TJ ET q 1 0 0 1 220.014 415.403 cm []0 d 0 J 0.44 w 0 0 m 6.695 0 l S Q BT /F51 8.2889 Tf 220.962 406.222 Td [(2)]TJ/F192 9.5641 Tf 6.942 6.79 Td [(;)]TJ/F52 8.2889 Tf 6.832 0 Td [(k)]TJ/F191 9.5641 Tf 6.967 0 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.192 0 Td [(n)]TJ/F191 9.5641 Tf 6.916 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(1)]TJ/F192 9.5641 Tf 4.8 0 Td [(:)]TJ ET 1 0 0 1 414.923 413.012 cm 0 g 0 G 1 0 0 1 -414.923 -413.012 cm BT /F51 8.2889 Tf 416.995 413.012 Td [(\0506\051)]TJ ET 1 0 0 1 427.92 413.012 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -413.012 cm BT /F51 8.2889 Tf 45.354 392.226 Td [(Then)-250(the)-250(2)]TJ/F52 8.2889 Tf 40.45 0 Td [(n)]TJ/F51 8.2889 Tf 6.863 0 Td [(triangles)-250(of)-250(the)-250(tessellation)-250(are)]TJ ET 1 0 0 1 45.354 392.226 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -17.364 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -374.862 cm BT /F52 8.2889 Tf 69.265 374.862 Td [(f)]TJ/F52 5.8022 Tf 4.165 3.95 Td [(k)]TJ -1.679 -6.523 Td [(k)]TJ/F192 9.5641 Tf 5.194 2.573 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(f)]TJ/F52 5.8022 Tf 4.165 3.95 Td [(k)]TJ -1.679 -6.523 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.573 Td [(;)]TJ/F52 8.2889 Tf 13.048 0 Td [(k)]TJ/F191 9.5641 Tf 6.967 0 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.192 0 Td [(n)]TJ/F191 9.5641 Tf 6.916 0 Td [(\000)]TJ/F51 8.2889 Tf 9.586 0 Td [(1)-250(\050mod)]TJ/F52 8.2889 Tf 29.326 0 Td [(n)]TJ/F51 8.2889 Tf 4.79 0 Td [(\051)]TJ/F192 9.5641 Tf 3.059 0 Td [(;)]TJ ET 1 0 0 1 414.923 374.862 cm 0 g 0 G 1 0 0 1 -414.923 -374.862 cm BT /F51 8.2889 Tf 416.995 374.862 Td [(\0507\051)]TJ ET 1 0 0 1 427.92 374.862 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -374.862 cm BT /F51 8.2889 Tf 45.354 356.075 Td [(where)-226(each)-226(of)]TJ/F52 8.2889 Tf 54.987 0 Td [(f)]TJ/F52 5.8022 Tf 4.165 3.572 Td [(k)]TJ -1.678 -6.264 Td [(k)]TJ/F51 8.2889 Tf 5.194 2.692 Td [(,)]TJ/F52 8.2889 Tf 3.812 0 Td [(f)]TJ/F52 5.8022 Tf 4.165 3.572 Td [(k)]TJ -1.678 -6.265 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F51 8.2889 Tf 5.73 2.693 Td [(is)-226(the)-226(triangle)-226(with)-226(vertices)]TJ/F52 8.2889 Tf 105.225 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(1)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)]TJ/F52 8.2889 Tf 4.759 0 Td [(p)]TJ/F52 5.8022 Tf 4.609 -1.434 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.434 Td [(,)-226(the)-226(edge)]TJ/F52 8.2889 Tf 38.178 0 Td [(e)]TJ/F52 5.8022 Tf 3.978 -1.434 Td [(k)]TJ/F51 8.2889 Tf 3.516 1.434 Td [(,)-226(or)]TJ/F52 8.2889 Tf 13.783 0 Td [(e)]TJ/F52 5.8022 Tf 3.979 -1.434 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F51 8.2889 Tf 3.858 1.434 Td [(,)-226(respectively,)-226(and)-226(the)]TJ ET 1 0 0 1 45.354 356.075 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -356.075 cm BT /F51 8.2889 Tf 45.354 345.614 Td [(other)-250(two)-250(edges)-250(given)-250(by)-250(the)-250(minimizing)-250(geodesics)-250(joining)]TJ/F52 8.2889 Tf 226.079 0 Td [(p)]TJ/F52 5.8022 Tf 4.608 -1.434 Td [(k)]TJ/F51 8.2889 Tf 5.588 1.434 Td [(and)]TJ/F52 8.2889 Tf 16.32 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(1)-250(\050see)]TJ ET 1 0 0 1 341.153 345.614 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -341.153 -345.614 cm BT /F51 8.2889 Tf 341.153 345.614 Td [(Fig.)]TJ ET 1 0 0 1 356.371 345.614 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -356.371 -345.614 cm BT /F51 8.2889 Tf 356.371 345.614 Td [(1)]TJ ET 1 0 0 1 361.17 345.614 cm 0 g 0 G 1 0 0 1 -361.17 -345.614 cm BT /F51 8.2889 Tf 361.17 345.614 Td [(\051.)]TJ ET 1 0 0 1 45.354 345.614 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -345.614 cm BT /F51 8.2889 Tf 57.31 334.889 Td [(Lifting)-264(this)-263(triangulation)-264(through)-264(the)-263(branched)-264(covering,)-264(we)-264(then)-263(get)-264(a)-264(triangulation)-263(for)]TJ/F52 8.2889 Tf 336.795 0 Td [(S)]TJ/F52 5.8022 Tf 4.062 -1.435 Td [(n)]TJ/F51 8.2889 Tf 3.852 1.435 Td [(.)-264(There)]TJ ET 1 0 0 1 45.354 334.889 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -334.889 cm BT /F51 8.2889 Tf 45.354 324.428 Td [(are)-250(3)]TJ/F52 8.2889 Tf 18.924 0 Td [(n)]TJ/F51 8.2889 Tf 6.863 0 Td [(vertices,)]TJ ET 1 0 0 1 45.354 324.428 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -17.364 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -307.064 cm BT /F52 8.2889 Tf 69.265 307.064 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(0)]TJ/F52 5.8022 Tf 4.8 -1.435 Td [(k)]TJ/F191 9.5641 Tf 6.171 1.435 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.932 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.74 0 Td [(.\031)]TJ/F191 6.6948 Tf 7.184 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(2)]TJ/F52 5.8022 Tf 3.359 0 Td [(k)]TJ/F192 6.6948 Tf 3.018 0 Td [(\031)-100(/=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F191 9.5641 Tf 3.851 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F52 8.2889 Tf 21.338 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(1)]TJ/F52 5.8022 Tf 4.8 -1.435 Td [(k)]TJ/F191 9.5641 Tf 6.171 1.435 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.932 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.\031)]TJ/F191 6.6948 Tf 7.183 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(2)]TJ/F52 5.8022 Tf 3.36 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(/=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(1)]TJ/F191 9.5641 Tf 4.799 0 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F52 8.2889 Tf 21.338 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(2)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(k)]TJ/F191 9.5641 Tf 6.172 1.435 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.932 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.\031)]TJ/F191 6.6948 Tf 7.183 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(2)]TJ/F52 5.8022 Tf 3.359 0 Td [(k)]TJ/F192 6.6948 Tf 3.018 0 Td [(\031)-100(/=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 3.851 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F191 9.5641 Tf 4.799 0 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ ET 1 0 0 1 45.354 307.064 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -307.064 cm BT /F51 8.2889 Tf 45.354 289.965 Td [(for)]TJ/F52 8.2889 Tf 14.655 0 Td [(k)]TJ/F191 9.5641 Tf 11.386 0 Td [(D)]TJ/F51 8.2889 Tf 14.536 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.192 0 Td [(n)]TJ/F191 9.5641 Tf 8.684 0 Td [(\000)]TJ/F51 8.2889 Tf 11.353 0 Td [(1)-458(\050mod)]TJ/F52 8.2889 Tf 31.05 0 Td [(n)]TJ/F51 8.2889 Tf 4.791 0 Td [(\051,)-458(and)-458(2)]TJ/F52 8.2889 Tf 31.639 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F51 8.2889 Tf 7.653 -3.472 Td [(triangles.)-459(It)-458(is)-458(not)-458(hard)-458(to)-458(see)-458(that)-458(these)-458(triangles,)-458(as)]TJ ET 1 0 0 1 45.354 289.965 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -289.965 cm BT /F51 8.2889 Tf 45.354 279.504 Td [(lifts)-329(of)]TJ/F52 8.2889 Tf 27.432 0 Td [(f)]TJ/F52 5.8022 Tf 4.165 3.572 Td [(k)]TJ -1.679 -6.264 Td [(k)]TJ/F192 9.5641 Tf 5.194 2.692 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(f)]TJ/F52 5.8022 Tf 4.165 3.572 Td [(k)]TJ -1.679 -6.265 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F51 8.2889 Tf 6.587 2.693 Td [(and)-329(expressed)-329(in)-330(terms)-329(of)-329(their)-329(vertices,)-329(are)]TJ/F191 9.5641 Tf 173.848 0 Td [(4)]TJ/F52 8.2889 Tf 7.498 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F52 8.2889 Tf 3.515 1.435 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(1)]TJ/F191 6.6948 Tf 4.799 -1.435 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F52 8.2889 Tf 3.857 1.435 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(2)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(k)]TJ/F192 9.5641 Tf 3.515 1.435 Td [(;)]TJ/F191 9.5641 Tf 4.76 0 Td [(4)]TJ/F52 8.2889 Tf 7.498 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F192 6.6948 Tf 5.222 0 Td [(.)]TJ/F52 5.8022 Tf 2.497 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(/)]TJ/F52 8.2889 Tf 2.995 1.435 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(1)]TJ/F191 6.6948 Tf 4.8 -1.435 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F52 8.2889 Tf 3.858 1.435 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(2)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.435 Td [(,)]TJ ET 1 0 0 1 45.354 279.504 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -279.504 cm BT /F51 8.2889 Tf 45.354 269.043 Td [(respectively.)-250(We)-250(denote)-250(them)-250(by)-250(the)-250(following:)]TJ ET 1 0 0 1 45.354 269.043 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -17.364 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -251.679 cm BT /F52 8.2889 Tf 69.265 251.679 Td [(b)]TJ/F52 5.8022 Tf 4.501 -1.434 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 9.5641 Tf 3.515 1.434 Td [(;)]TJ/F52 8.2889 Tf 21.337 0 Td [(b)]TJ/F52 5.8022 Tf 4.501 -1.434 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F192 6.6948 Tf 5.222 0 Td [(.)]TJ/F52 5.8022 Tf 2.497 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(/;)]TJ/F191 6.6948 Tf 4.714 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 9.5641 Tf 3.515 1.434 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(j)]TJ/F192 9.5641 Tf 2.395 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(k)]TJ/F191 9.5641 Tf 6.967 0 Td [(D)]TJ/F51 8.2889 Tf 10.116 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.191 0 Td [(n)]TJ/F191 9.5641 Tf 6.917 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(1)-250(\050mod)]TJ/F52 8.2889 Tf 29.326 0 Td [(n)]TJ/F51 8.2889 Tf 4.791 0 Td [(\051)]TJ/F192 9.5641 Tf 3.058 0 Td [(:)]TJ ET 1 0 0 1 414.923 251.679 cm 0 g 0 G 1 0 0 1 -414.923 -251.679 cm BT /F51 8.2889 Tf 416.995 251.679 Td [(\0508\051)]TJ ET 1 0 0 1 427.92 251.679 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -251.679 cm BT /F51 8.2889 Tf 45.354 234.58 Td [(To)-250(be)-250(more)-250(clear,)-250(we)-250(verify)-250(the)-250(indices)-250(in)]TJ ET 1 0 0 1 203.53 234.58 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -203.53 -234.58 cm BT /F51 8.2889 Tf 203.53 234.58 Td [(\050)]TJ ET 1 0 0 1 206.597 234.58 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -206.597 -234.58 cm BT /F51 8.2889 Tf 206.597 234.58 Td [(8)]TJ ET 1 0 0 1 211.396 234.58 cm 0 g 0 G 1 0 0 1 -211.396 -234.58 cm BT /F51 8.2889 Tf 211.396 234.58 Td [(\051)-250(by)-250(showing)-250(the)-250(edges)-250(of)-250(these)-250(triangles)-250(explicitly.)]TJ ET 1 0 0 1 45.354 234.58 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -234.58 cm BT /F51 8.2889 Tf 57.31 223.854 Td [(The)-396(three)-396(edges)-396(of)]TJ/F52 8.2889 Tf 76.67 0 Td [(b)]TJ/F52 5.8022 Tf 4.501 -1.434 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F192 6.6948 Tf 5.222 0 Td [(.)]TJ/F52 5.8022 Tf 2.497 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(/;)]TJ/F191 6.6948 Tf 4.713 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.434 Td [(,)-396(in)-396(the)-396(order)]TJ/F52 8.2889 Tf 55.842 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(2)]TJ/F52 5.8022 Tf 4.799 -1.434 Td [(k)]TJ ET q 1 0 0 1 255.361 226.245 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 260.701 223.854 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ/F52 5.8022 Tf 4.799 -1.434 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F192 6.6948 Tf 5.222 0 Td [(.)]TJ/F52 5.8022 Tf 2.497 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(/)]TJ ET q 1 0 0 1 295.294 226.245 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 300.634 223.854 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(1)]TJ/F191 6.6948 Tf 4.799 -1.434 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ ET q 1 0 0 1 327.216 226.245 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 332.556 223.854 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(2)]TJ/F52 5.8022 Tf 4.799 -1.434 Td [(k)]TJ/F51 8.2889 Tf 3.516 1.434 Td [(,)-396(can)-396(be)-396(described)-396(as)]TJ -300.125 -12.473 Td [(follows:)-358(notice)-358(that)-358(the)-358(first)-358(two)-358(coordinates)-358(give)-358(the)-358(edges)-358(of)]TJ/F52 8.2889 Tf 247.709 0 Td [(f)]TJ/F52 5.8022 Tf 4.165 3.572 Td [(k)]TJ -1.678 -6.265 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F51 8.2889 Tf 3.857 2.693 Td [(,)-358(in)-358(the)-358(order)]TJ/F52 8.2889 Tf 54.584 0 Td [(p)]TJ/F52 5.8022 Tf 4.609 -1.434 Td [(k)]TJ ET q 1 0 0 1 371.549 213.772 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 376.889 211.381 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ/F52 5.8022 Tf 5.995 4.88 Td [(e)]TJ/F52 4.9734 Tf 2.785 -1.353 Td [(k)]TJ/F191 5.7385 Tf 2.586 0 Td [(C)]TJ/F51 4.9734 Tf 4.476 0 Td [(1)]TJ ET q 1 0 0 1 387.493 213.772 cm []0 d 0 J 0.44 w 0 0 m 13.225 0 l S Q BT /F52 8.2889 Tf 401.913 211.381 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(1)]TJ ET q 1 0 0 1 412.516 213.772 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 417.856 211.381 Td [(p)]TJ/F52 5.8022 Tf 4.609 -1.434 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.434 Td [(,)]TJ -380.626 -12.415 Td [(and)-250(the)-250(factor)-250(e)]TJ/F51 5.8022 Tf 59.514 3.472 Td [(i2)]TJ/F52 5.8022 Tf 5.1 0 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(\031)-100(=)]TJ/F52 5.8022 Tf 7.833 0 Td [(n)]TJ/F51 8.2889 Tf 5.924 -3.472 Td [(on)-250(the)-250(third)-250(coordinate)-250(specifies)-250(a)-250(certain)-250(branch)-250(to)-250(which)]TJ/F52 8.2889 Tf 224.42 0 Td [(f)]TJ/F52 5.8022 Tf 4.166 3.572 Td [(k)]TJ -1.679 -6.265 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F51 8.2889 Tf 5.93 2.693 Td [(is)-250(lifted.)]TJ/F191 9.5641 Tf -289.164 -19.037 Td [(T)]TJ/F51 8.2889 Tf 3.185 0 Td [(cos)]TJ/F52 8.2889 Tf 13.961 0 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(sin)]TJ/F52 8.2889 Tf 12.8 0 Td [(t)]TJ/F51 8.2889 Tf 5.237 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.)]TJ/F51 5.8022 Tf 2.497 0 Td [(2)]TJ/F52 5.8022 Tf 3.359 0 Td [(k)]TJ/F191 6.6948 Tf 3.018 0 Td [(C)]TJ/F51 5.8022 Tf 5.221 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(/\031)-100(=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(e)]TJ/F51 5.8022 Tf 4.359 3.95 Td [(i2)]TJ/F52 5.8022 Tf 5.101 0 Td [(j)]TJ/F192 6.6948 Tf 1.676 0 Td [(\031)-100(=)]TJ/F52 5.8022 Tf 7.833 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(.)]TJ/F191 9.5641 Tf 3.567 0 Td [(\000)]TJ/F51 8.2889 Tf 9.054 0 Td [(cos)]TJ/F52 5.8022 Tf 12.367 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.95 Td [(t)]TJ/F191 9.5641 Tf 5.768 0 Td [(C)]TJ/F51 8.2889 Tf 9.586 0 Td [(sin)]TJ/F52 5.8022 Tf 11.206 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.95 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(/)]TJ/F51 5.8022 Tf 3.567 3.95 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(=)]TJ/F52 5.8022 Tf 3.146 0 Td [(n)]TJ/F191 9.5641 Tf 3.852 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)-1033(\031)-100(=)]TJ/F51 8.2889 Tf 24.238 0 Td [(4)]TJ/F191 9.5641 Tf 7.456 0 Td [(\024)]TJ/F52 8.2889 Tf 9.868 0 Td [(t)]TJ/F191 9.5641 Tf 6.3 0 Td [(\024)]TJ/F192 9.5641 Tf 9.868 0 Td [(\031)-100(=)]TJ/F51 8.2889 Tf 11.19 0 Td [(2)]TJ/F191 9.5641 Tf 4.799 0 Td [(I)]TJ -265.817 -14.466 Td [(T)]TJ/F51 8.2889 Tf 3.185 0 Td [(sin)]TJ/F52 8.2889 Tf 12.801 0 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(cos)]TJ/F52 8.2889 Tf 13.961 0 Td [(t)]TJ/F51 8.2889 Tf 5.237 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i2)]TJ/F192 6.6948 Tf 5.1 0 Td [(.)]TJ/F52 5.8022 Tf 2.497 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(/\031)-100(=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i2)]TJ/F52 5.8022 Tf 5.1 0 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(\031)-100(=)]TJ/F52 5.8022 Tf 7.833 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(.)]TJ/F191 9.5641 Tf 3.567 0 Td [(\000)]TJ/F51 8.2889 Tf 9.054 0 Td [(sin)]TJ/F52 5.8022 Tf 11.207 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.95 Td [(t)]TJ/F191 9.5641 Tf 5.768 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(cos)]TJ/F52 5.8022 Tf 12.367 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.95 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(/)]TJ/F51 5.8022 Tf 3.567 3.95 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(=)]TJ/F52 5.8022 Tf 3.146 0 Td [(n)]TJ/F191 9.5641 Tf 3.852 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F51 8.2889 Tf 13.048 0 Td [(0)]TJ/F191 9.5641 Tf 7.456 0 Td [(\024)]TJ/F52 8.2889 Tf 9.868 0 Td [(t)]TJ/F191 9.5641 Tf 6.3 0 Td [(\024)]TJ/F192 9.5641 Tf 9.868 0 Td [(\031)-100(=)]TJ/F51 8.2889 Tf 11.19 0 Td [(2)]TJ/F191 9.5641 Tf 4.799 0 Td [(I)]TJ ET 1 0 0 1 414.923 165.463 cm 0 g 0 G 1 0 0 1 -414.923 -165.463 cm BT /F51 8.2889 Tf 416.995 165.463 Td [(\0509\051)]TJ ET 1 0 0 1 427.92 165.463 cm 0 g 0 G 1 0 0 1 -427.92 -165.463 cm BT /F191 9.5641 Tf 77.314 150.997 Td [(T)]TJ/F51 8.2889 Tf 3.185 0 Td [(cos)]TJ/F52 8.2889 Tf 13.961 0 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(sin)]TJ/F52 8.2889 Tf 12.8 0 Td [(t)]TJ/F51 8.2889 Tf 5.237 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.)]TJ/F51 5.8022 Tf 2.497 0 Td [(2)]TJ/F52 5.8022 Tf 3.359 0 Td [(k)]TJ/F191 6.6948 Tf 3.018 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(/\031)-100(=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i2)]TJ/F52 5.8022 Tf 5.1 0 Td [(j)]TJ/F192 6.6948 Tf 1.676 0 Td [(\031)-100(=)]TJ/F52 5.8022 Tf 7.833 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(.)]TJ/F191 9.5641 Tf 3.567 0 Td [(\000)]TJ/F51 8.2889 Tf 9.054 0 Td [(cos)]TJ/F52 5.8022 Tf 12.367 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.95 Td [(t)]TJ/F191 9.5641 Tf 5.768 0 Td [(C)]TJ/F51 8.2889 Tf 9.586 0 Td [(sin)]TJ/F52 5.8022 Tf 11.206 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.95 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(/)]TJ/F51 5.8022 Tf 3.567 3.95 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(=)]TJ/F52 5.8022 Tf 3.146 0 Td [(n)]TJ/F191 9.5641 Tf 3.852 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F51 8.2889 Tf 13.049 0 Td [(0)]TJ/F191 9.5641 Tf 7.455 0 Td [(\024)]TJ/F52 8.2889 Tf 9.868 0 Td [(t)]TJ/F191 9.5641 Tf 6.3 0 Td [(\024)]TJ/F192 9.5641 Tf 9.868 0 Td [(\031)-100(=)]TJ/F51 8.2889 Tf 11.19 0 Td [(4)]TJ/F192 9.5641 Tf 4.799 0 Td [(:)]TJ/F51 8.2889 Tf -286.587 -16.703 Td [(Similarly,)-270(the)-270(three)-270(edges)-271(of)]TJ/F52 8.2889 Tf 109.353 0 Td [(b)]TJ/F52 5.8022 Tf 4.5 -1.435 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F51 8.2889 Tf 3.516 1.435 Td [(,)-270(in)-270(the)-270(order)]TJ/F52 8.2889 Tf 51.669 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(2)]TJ/F52 5.8022 Tf 4.8 -1.435 Td [(k)]TJ ET q 1 0 0 1 258.339 136.685 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 263.679 134.294 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(1)]TJ/F191 6.6948 Tf 4.799 -1.435 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ ET q 1 0 0 1 290.26 136.685 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 295.6 134.294 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ ET q 1 0 0 1 316.618 136.685 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 321.958 134.294 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(2)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(k)]TJ/F51 8.2889 Tf 3.516 1.435 Td [(,)-270(as)-270(lifts)-270(of)-271(those)-270(of)]TJ/F52 8.2889 Tf 73.67 0 Td [(f)]TJ/F52 5.8022 Tf 4.165 3.571 Td [(k)]TJ -1.679 -6.263 Td [(k)]TJ/F51 8.2889 Tf 5.194 2.692 Td [(,)-270(in)]TJ -370.877 -12.041 Td [(the)-250(order)]TJ/F52 8.2889 Tf 37.408 0 Td [(p)]TJ/F52 5.8022 Tf 4.608 -1.435 Td [(k)]TJ ET q 1 0 0 1 92.081 124.644 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 97.421 122.253 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(1)]TJ/F52 5.8022 Tf 5.995 4.448 Td [(e)]TJ/F52 4.9734 Tf 2.785 -1.352 Td [(k)]TJ ET q 1 0 0 1 108.025 124.644 cm []0 d 0 J 0.44 w 0 0 m 5.869 0 l S Q BT /F52 8.2889 Tf 115.089 122.253 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ ET q 1 0 0 1 125.693 124.644 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 131.033 122.253 Td [(p)]TJ/F52 5.8022 Tf 4.608 -1.435 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.435 Td [(,)-250(are)]TJ/F191 9.5641 Tf -61.842 -19.183 Td [(T)]TJ/F51 8.2889 Tf 3.185 0 Td [(sin)]TJ/F52 8.2889 Tf 12.801 0 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(cos)]TJ/F52 8.2889 Tf 13.961 0 Td [(t)]TJ/F51 8.2889 Tf 5.237 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.)]TJ/F51 5.8022 Tf 2.497 0 Td [(2)]TJ/F52 5.8022 Tf 3.359 0 Td [(k)]TJ/F191 6.6948 Tf 3.018 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(/\031)-100(=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i2)]TJ/F52 5.8022 Tf 5.1 0 Td [(j)]TJ/F192 6.6948 Tf 1.676 0 Td [(\031)-100(=)]TJ/F52 5.8022 Tf 7.833 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(.)]TJ/F191 9.5641 Tf 3.567 0 Td [(\000)]TJ/F51 8.2889 Tf 9.054 0 Td [(sin)]TJ/F52 5.8022 Tf 11.207 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.95 Td [(t)]TJ/F191 9.5641 Tf 5.768 0 Td [(C)]TJ/F51 8.2889 Tf 9.585 0 Td [(cos)]TJ/F52 5.8022 Tf 12.367 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.95 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(/)]TJ/F51 5.8022 Tf 3.567 3.95 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(=)]TJ/F52 5.8022 Tf 3.146 0 Td [(n)]TJ/F191 9.5641 Tf 3.852 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)-1033(\031)-100(=)]TJ/F51 8.2889 Tf 24.239 0 Td [(4)]TJ/F191 9.5641 Tf 7.455 0 Td [(\024)]TJ/F52 8.2889 Tf 9.868 0 Td [(t)]TJ/F191 9.5641 Tf 6.3 0 Td [(\024)]TJ/F192 9.5641 Tf 9.868 0 Td [(\031)-100(=)]TJ/F51 8.2889 Tf 11.19 0 Td [(2)]TJ/F191 9.5641 Tf 4.799 0 Td [(I)]TJ -265.817 -13.45 Td [(T)]TJ/F51 8.2889 Tf 3.185 0 Td [(cos)]TJ/F52 8.2889 Tf 13.961 0 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(sin)]TJ/F52 8.2889 Tf 12.8 0 Td [(t)]TJ/F51 8.2889 Tf 5.237 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i2)]TJ/F52 5.8022 Tf 5.1 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(=)]TJ/F52 5.8022 Tf 7.833 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i2)]TJ/F52 5.8022 Tf 5.1 0 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(\031)-100(=)]TJ/F52 5.8022 Tf 7.832 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(.)]TJ/F191 9.5641 Tf 3.568 0 Td [(\000)]TJ/F51 8.2889 Tf 9.054 0 Td [(cos)]TJ/F52 5.8022 Tf 12.367 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.445 -3.95 Td [(t)]TJ/F191 9.5641 Tf 5.769 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(sin)]TJ/F52 5.8022 Tf 11.206 3.95 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.95 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(/)]TJ/F51 5.8022 Tf 3.568 3.95 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(=)]TJ/F52 5.8022 Tf 3.147 0 Td [(n)]TJ/F191 9.5641 Tf 3.851 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F51 8.2889 Tf 13.049 0 Td [(0)]TJ/F191 9.5641 Tf 7.456 0 Td [(\024)]TJ/F52 8.2889 Tf 9.868 0 Td [(t)]TJ/F191 9.5641 Tf 6.299 0 Td [(\024)]TJ/F192 9.5641 Tf 9.868 0 Td [(\031)-100(=)]TJ/F51 8.2889 Tf 11.19 0 Td [(2)]TJ/F191 9.5641 Tf 4.799 0 Td [(I)]TJ ET 1 0 0 1 410.124 89.62 cm 0 g 0 G 1 0 0 1 -410.124 -89.62 cm BT /F51 8.2889 Tf 412.196 89.62 Td [(\05010\051)]TJ ET 1 0 0 1 427.92 89.62 cm 0 g 0 G 1 0 0 1 -427.92 -89.62 cm BT /F191 9.5641 Tf 77.314 75.154 Td [(T)]TJ/F51 8.2889 Tf 3.185 0 Td [(sin)]TJ/F52 8.2889 Tf 12.801 0 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(cos)]TJ/F52 8.2889 Tf 13.961 0 Td [(t)]TJ/F51 8.2889 Tf 5.237 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.)]TJ/F51 5.8022 Tf 2.497 0 Td [(2)]TJ/F52 5.8022 Tf 3.359 0 Td [(k)]TJ/F191 6.6948 Tf 3.018 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(/\031)-100(=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 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[(n)]TJ/F51 8.2889 Tf 6.061 1.434 Td [(described)-267(in)-266(Section)]TJ ET 1 0 0 1 316.868 440.739 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -316.868 -440.739 cm BT /F51 8.2889 Tf 316.868 440.739 Td [(1)]TJ ET 1 0 0 1 321.668 440.739 cm 0 g 0 G 1 0 0 1 -321.668 -440.739 cm BT /F51 8.2889 Tf 323.877 440.739 Td [(to)-267(a)-266(tessellation)-267(of)-266(the)]TJ/F144 8.6077 Tf 86.823 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 3.858 -3.472 Td [(.)]TJ ET 1 0 0 1 45.354 440.739 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -440.739 cm BT /F51 8.2889 Tf 45.354 430.279 Td [(Then,)-250(by)-250(lifting,)-250(that)-250(will)-250(automatically)-250(produce)-250(a)-250(tessellation)-250(of)]TJ/F52 8.2889 Tf 245.052 0 Td [(F)]TJ/F52 5.8022 Tf 4.028 -1.435 Td [(n)]TJ/F51 8.2889 Tf 3.852 1.435 Td [(.)]TJ ET 1 0 0 1 45.354 430.279 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -430.279 cm BT /F51 8.2889 Tf 57.31 419.708 Td [(Denote)-250(the)-250(projective)-250(line)]TJ/F52 8.2889 Tf 100.941 0 Td [(z)]TJ/F52 5.8022 Tf 3.713 -1.435 Td [(j)]TJ/F191 9.5641 Tf 4.832 1.435 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)-250(by)]TJ/F52 8.2889 Tf 18.285 0 Td [(L)]TJ/F52 5.8022 Tf 3.929 -1.435 Td [(j)]TJ/F51 8.2889 Tf 2.175 1.435 Td [(,)-250(for)]TJ/F52 8.2889 Tf 16.942 0 Td [(j)]TJ/F191 9.5641 Tf 5.052 0 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(2,)-250(and)-250(let)]TJ ET 1 0 0 1 45.354 419.708 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -16.59 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -403.118 cm BT /F52 8.2889 Tf 69.265 403.118 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(01)]TJ/F191 9.5641 Tf 12.255 0 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.932 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(1)]TJ/F191 9.5641 Tf 4.799 0 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(12)]TJ/F191 9.5641 Tf 12.255 0 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.932 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F191 9.5641 Tf 4.799 0 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F52 8.2889 Tf 13.048 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(20)]TJ/F191 9.5641 Tf 12.255 0 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.932 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F191 9.5641 Tf 4.799 0 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(:)]TJ ET 1 0 0 1 410.124 403.118 cm 0 g 0 G 1 0 0 1 -410.124 -403.118 cm BT /F51 8.2889 Tf 412.196 403.118 Td [(\05011\051)]TJ ET 1 0 0 1 427.92 403.118 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -403.118 cm BT /F51 8.2889 Tf 57.31 386.638 Td [(We)-250(start)-250(by)-250(specifying)-250(the)-250(other)-250(2-cells)-250(for)-250(the)-250(tessellation.)]TJ ET 1 0 0 1 45.354 386.638 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -386.638 cm BT /F51 8.2889 Tf 57.31 376.068 Td [(Note)-177(that)-177(on)]TJ/F52 8.2889 Tf 47.881 0 Td [(L)]TJ/F51 5.8022 Tf 3.929 -1.435 Td [(0)]TJ/F51 8.2889 Tf 3.857 1.435 Td [(,)-177(the)-177(points)]TJ/F52 8.2889 Tf 42.768 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(01)]TJ/F192 9.5641 Tf 9.598 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(20)-177(and)-177(the)-177(intersections)-176(with)-177(the)]TJ/F52 8.2889 Tf 124.699 0 Td [(S)]TJ/F52 5.8022 Tf 4.061 -1.435 Td [(n)]TJ/F51 8.2889 Tf 3.852 1.435 Td [(,)-177(namely)]TJ/F52 8.2889 Tf 33.253 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(k)]TJ/F192 9.5641 Tf 3.515 1.435 Td [(;)]TJ/F52 8.2889 Tf 6.226 0 Td [(k)]TJ/F191 9.5641 Tf 6.967 0 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.192 0 Td [(n)]TJ/F191 9.5641 Tf 5.051 0 Td [(\000)]TJ/F51 8.2889 Tf 7.72 0 Td [(1,)]TJ ET 1 0 0 1 45.354 376.068 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -376.068 cm BT /F51 8.2889 Tf 45.354 365.607 Td [(form)-365(the)-364(exact)-365(same)-364(configuration)-365(as)]TJ ET 1 0 0 1 194.25 365.607 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -194.25 -365.607 cm BT /F51 8.2889 Tf 194.25 365.607 Td [(\050)]TJ ET 1 0 0 1 197.317 365.607 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -197.317 -365.607 cm BT /F51 8.2889 Tf 197.317 365.607 Td [(5)]TJ ET 1 0 0 1 202.116 365.607 cm 0 g 0 G 1 0 0 1 -202.116 -365.607 cm BT /F51 8.2889 Tf 202.116 365.607 Td [(\051)-365(and)-364(\050)]TJ ET 1 0 0 1 228.534 365.607 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -228.534 -365.607 cm BT /F51 8.2889 Tf 228.534 365.607 Td [(4)]TJ ET 1 0 0 1 233.333 365.607 cm 0 g 0 G 1 0 0 1 -233.333 -365.607 cm BT /F51 8.2889 Tf 233.333 365.607 Td [(\051)-365(on)]TJ/F144 8.6077 Tf 18.825 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(1)]TJ/F51 8.2889 Tf 6.879 -3.472 Td [(described)-365(in)-364(Section)]TJ ET 1 0 0 1 351.953 365.607 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -351.953 -365.607 cm BT /F51 8.2889 Tf 351.953 365.607 Td [(1)]TJ ET 1 0 0 1 356.752 365.607 cm 0 g 0 G 1 0 0 1 -356.752 -365.607 cm BT /F51 8.2889 Tf 356.752 365.607 Td [(.)-365(We)-365(then)-364(add)-365(the)]TJ ET 1 0 0 1 45.354 365.607 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -365.607 cm BT /F51 8.2889 Tf 45.354 355.146 Td [(corresponding)-221(2)]TJ/F52 8.2889 Tf 61.77 0 Td [(n)]TJ/F51 8.2889 Tf 6.624 0 Td [(triangles)]TJ ET 1 0 0 1 148.902 355.146 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -148.902 -355.146 cm BT /F51 8.2889 Tf 148.902 355.146 Td [(\050)]TJ ET 1 0 0 1 151.969 355.146 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -151.969 -355.146 cm BT /F51 8.2889 Tf 151.969 355.146 Td [(7)]TJ ET 1 0 0 1 156.768 355.146 cm 0 g 0 G 1 0 0 1 -156.768 -355.146 cm BT /F51 8.2889 Tf 156.768 355.146 Td [(\051;)-221(similarly)-221(for)-221(the)-222(lines)]TJ/F52 8.2889 Tf 90.065 0 Td [(L)]TJ/F51 5.8022 Tf 3.929 -1.435 Td [(1)]TJ/F51 8.2889 Tf 5.69 1.435 Td [(and)]TJ/F52 8.2889 Tf 16.082 0 Td [(L)]TJ/F51 5.8022 Tf 3.929 -1.435 Td [(2)]TJ/F51 8.2889 Tf 3.857 1.435 Td [(.)-221(Therefore)-221(altogether)-222(there)-221(are)-221(6)]TJ/F52 8.2889 Tf 124.473 0 Td [(n)]TJ/F51 8.2889 Tf 6.624 0 Td [(new)]TJ ET 1 0 0 1 45.354 355.146 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -355.146 cm BT /F51 8.2889 Tf 45.354 344.685 Td [(triangles,)-250(which)-250(we)-250(label)-250(as)-250(follows:)]TJ ET 1 0 0 1 45.354 344.685 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -16.59 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -328.095 cm BT /F52 8.2889 Tf 69.265 328.095 Td [(fj)]TJ/F52 5.8022 Tf 6.476 3.95 Td [(k)]TJ 0 -6.522 Td [(k)]TJ/F192 9.5641 Tf 3.515 2.572 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(fj)]TJ/F52 5.8022 Tf 6.476 3.95 Td [(k)]TJ 0 -6.522 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.857 2.572 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(j)]TJ/F191 9.5641 Tf 5.052 0 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(2)-1000(and)]TJ/F52 8.2889 Tf 35.625 0 Td [(k)]TJ/F191 9.5641 Tf 6.967 0 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.192 0 Td [(n)]TJ/F191 9.5641 Tf 6.916 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(1)-250(\050mod)]TJ/F52 8.2889 Tf 29.326 0 Td [(n)]TJ/F51 8.2889 Tf 4.791 0 Td [(\051)]TJ/F192 9.5641 Tf 3.059 0 Td [(:)]TJ ET 1 0 0 1 410.124 328.095 cm 0 g 0 G 1 0 0 1 -410.124 -328.095 cm BT /F51 8.2889 Tf 412.196 328.095 Td [(\05012\051)]TJ ET 1 0 0 1 427.92 328.095 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -328.095 cm BT /F51 8.2889 Tf 45.354 311.616 Td [(Label)-336(the)-335(edges)-336(corresponding)-335(to)-336(those)-336(in)]TJ ET 1 0 0 1 210.52 311.616 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -210.52 -311.616 cm BT /F51 8.2889 Tf 210.52 311.616 Td [(\050)]TJ ET 1 0 0 1 213.587 311.616 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -213.587 -311.616 cm BT /F51 8.2889 Tf 213.587 311.616 Td [(6)]TJ ET 1 0 0 1 218.386 311.616 cm 0 g 0 G 1 0 0 1 -218.386 -311.616 cm BT /F51 8.2889 Tf 218.386 311.616 Td [(\051)-336(by)]TJ/F52 8.2889 Tf 17.964 0 Td [(ej)]TJ/F52 5.8022 Tf 7.968 -1.435 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.435 Td [(.)-336(Notice)-336(that,)-335(for)-336(example,)-336(as)-335(a)-336(path,)]TJ/F52 8.2889 Tf 143.486 0 Td [(e)]TJ/F51 8.2889 Tf 3.978 0 Td [(1)]TJ/F52 5.8022 Tf 6.394 -1.435 Td [(k)]TJ/F192 9.5641 Tf 3.515 1.435 Td [(.)]TJ/F52 8.2889 Tf 3.567 0 Td [(t)]TJ/F192 9.5641 Tf 3.643 0 Td [(/)]TJ/F191 9.5641 Tf 8.044 0 Td [(D)]TJ ET 1 0 0 1 45.354 311.616 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -311.616 cm BT /F191 9.5641 Tf 45.354 301.155 Td [(T)]TJ/F51 8.2889 Tf 3.185 0 Td [(sin)]TJ/F52 8.2889 Tf 12.801 0 Td [(t)]TJ/F51 8.2889 Tf 5.237 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.472 Td [(i2)]TJ/F52 5.8022 Tf 5.1 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(=)]TJ/F52 5.8022 Tf 7.833 0 Td [(n)]TJ/F192 9.5641 Tf 3.851 -3.472 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(cos)]TJ/F52 8.2889 Tf 13.961 0 Td [(t)]TJ/F191 9.5641 Tf 3.643 0 Td [(U)]TJ/F51 8.2889 Tf 3.185 0 Td [(.)]TJ ET 1 0 0 1 45.354 301.155 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -301.155 cm BT /F51 8.2889 Tf 57.31 290.584 Td [(In)-378(the)-379(next)-378(group,)-379(each)-379(triangle)-378(is)-379(formed)-378(by)-379(minimizing)-378(geodesics)-379(joining)-378(one)-379(of)-378(the)-379(vertices)]TJ ET 1 0 0 1 45.354 290.584 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -290.584 cm BT /F52 8.2889 Tf 45.354 280.123 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(01)]TJ/F192 9.5641 Tf 9.598 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(12)]TJ/F192 9.5641 Tf 9.598 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(20)-349(to)-348(the)-349(edge)-349(on)]TJ/F52 8.2889 Tf 72.185 0 Td [(S)]TJ/F52 5.8022 Tf 4.061 -1.434 Td [(n)]TJ/F51 8.2889 Tf 3.852 1.434 Td [(,)-349(e.g.,)]TJ/F52 8.2889 Tf 22.41 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(2)]TJ/F52 5.8022 Tf 4.799 -1.434 Td [(j)]TJ ET q 1 0 0 1 203.182 282.514 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 208.522 280.123 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(0)]TJ/F52 5.8022 Tf 4.799 -1.434 Td [(k)]TJ/F51 8.2889 Tf 6.406 1.434 Td [(in)-349(the)-348(case)-349(of)]TJ/F52 8.2889 Tf 55.327 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(20.)-349(We)-349(denote)-349(these)-348(3)]TJ/F52 8.2889 Tf 87.907 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F51 8.2889 Tf 6.748 -3.472 Td [(triangles)-349(as)]TJ ET 1 0 0 1 45.354 280.123 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -280.123 cm BT /F51 8.2889 Tf 45.354 269.663 Td [(follows:)]TJ ET 1 0 0 1 45.354 269.663 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -16.59 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -253.073 cm BT /F52 8.2889 Tf 69.265 253.073 Td [(h)]TJ/F51 8.2889 Tf 4.675 0 Td [(01)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(jk)]TJ/F192 9.5641 Tf 5.192 1.435 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(h)]TJ/F51 8.2889 Tf 4.675 0 Td [(12)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(jk)]TJ/F192 9.5641 Tf 5.192 1.435 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(h)]TJ/F51 8.2889 Tf 4.675 0 Td [(20)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(jk)]TJ/F192 9.5641 Tf 5.192 1.435 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(j)]TJ/F192 9.5641 Tf 2.395 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(k)]TJ/F191 9.5641 Tf 6.967 0 Td [(D)]TJ/F51 8.2889 Tf 10.116 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.191 0 Td [(n)]TJ/F191 9.5641 Tf 6.917 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(1)-250(\050mod)]TJ/F52 8.2889 Tf 29.326 0 Td [(n)]TJ/F51 8.2889 Tf 4.791 0 Td [(\051)]TJ/F192 9.5641 Tf 3.058 0 Td [(:)]TJ ET 1 0 0 1 410.124 253.073 cm 0 g 0 G 1 0 0 1 -410.124 -253.073 cm BT /F51 8.2889 Tf 412.196 253.073 Td [(\05013\051)]TJ ET 1 0 0 1 427.92 253.073 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -253.073 cm BT /F51 8.2889 Tf 57.31 236.593 Td [(We)-285(remark)-286(that)-285(all)-286(the)-285(triangles)-285(in)]TJ ET 1 0 0 1 192.667 236.593 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -192.667 -236.593 cm BT /F51 8.2889 Tf 192.667 236.593 Td [(\050)]TJ ET 1 0 0 1 195.734 236.593 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -195.734 -236.593 cm BT /F51 8.2889 Tf 195.734 236.593 Td [(13)]TJ ET 1 0 0 1 205.332 236.593 cm 0 g 0 G 1 0 0 1 -205.332 -236.593 cm BT /F51 8.2889 Tf 205.332 236.593 Td [(\051)-285(are)-286(totally)-285(geodesic;)-286(one)-285(sees,)-286(e.g.,)-285(from)]TJ ET 1 0 0 1 365.328 236.593 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -365.328 -236.593 cm BT /F51 8.2889 Tf 365.328 236.593 Td [(\050)]TJ ET 1 0 0 1 368.395 236.593 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -368.395 -236.593 cm BT /F51 8.2889 Tf 368.395 236.593 Td [(9)]TJ ET 1 0 0 1 373.194 236.593 cm 0 g 0 G 1 0 0 1 -373.194 -236.593 cm BT /F51 8.2889 Tf 373.194 236.593 Td [(\051)-285(that)-286(they)-285(are)]TJ ET 1 0 0 1 45.354 236.593 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -236.593 cm BT /F51 8.2889 Tf 45.354 226.132 Td [(pieces)-250(of)-250(real)-250(projective)-250(planes.)-250(In)-250(fact,)-250(all)-250(the)-250(new)-250(2-cells)-250(we)-250(add)-250(will)-250(be)-250(totally)-250(geodesic.)]TJ ET 1 0 0 1 45.354 226.132 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -226.132 cm BT /F51 8.2889 Tf 57.31 215.561 Td [(There)-336(is)-336(one)-336(more)-336(group)-335(of)]TJ/F52 8.2889 Tf 108.869 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F51 8.2889 Tf 6.642 -3.472 Td [(triangles)-336(that)-336(all)-336(have)-336(the)-335(same)-336(three)-336(vertices)]TJ/F52 8.2889 Tf 181.113 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(01)]TJ/F192 9.5641 Tf 9.599 0 Td [(;)]TJ/F52 8.2889 Tf 4.759 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(12)]TJ/F192 9.5641 Tf 9.598 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(p)]TJ/F51 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[(noticing)-299(again)-298(that)-299(any)-299(one)-299(of)-298(the)-299(indices)-299(of)]TJ/F52 8.2889 Tf 171.94 0 Td [(g)]TJ/F51 8.2889 Tf 7.478 0 Td [(is)-299(determined)-298(by)-299(the)-299(other)-299(two)-298(according)-299(to)-299(the)-298(rule)]TJ ET 1 0 0 1 45.354 138.961 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -138.961 cm BT /F51 8.2889 Tf 45.354 128.501 Td [(that)-250(the)-250(sum)-250(of)-250(the)-250(three)-250(indices)-250(is)-250(equal)-250(to)-250(0.)]TJ ET 1 0 0 1 45.354 128.501 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -128.501 cm BT /F51 8.2889 Tf 57.31 117.93 Td [(The)-292(next)-292(set)-293(of)-292(2-cells)-292(is)-292(a)-292(set)-293(of)-292(3)]TJ/F52 8.2889 Tf 130.564 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F51 8.2889 Tf 6.28 -3.472 Td [(quadrilaterals.)-292(They)-293(are)-292(in)-292(one-to-one)-292(correspondence)-292(with)]TJ ET 1 0 0 1 45.354 117.93 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -117.93 cm BT /F51 8.2889 Tf 45.354 107.469 Td [(the)-291(edges)-290(in)]TJ/F52 8.2889 Tf 49.054 0 Td [(S)]TJ/F52 5.8022 Tf 4.062 -1.434 Td [(n)]TJ/F51 8.2889 Tf 3.851 1.434 Td [(;)-291(each)-290(edge)-291(is)-291(one)-290(side)-291(of)-291(exactly)-290(one)-291(quadrilateral.)-291(For)-291(example,)-290(the)-291(edge)]TJ/F52 8.2889 Tf 285.965 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(0)]TJ/F52 5.8022 Tf 4.799 -1.434 Td [(j)]TJ ET q 1 0 0 1 401.064 109.86 cm []0 d 0 J 0.44 w 0 0 m 4.144 0 l S Q BT /F52 8.2889 Tf 406.404 107.469 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(1)]TJ/F52 5.8022 Tf 4.8 -1.434 Td [(k)]TJ/F51 8.2889 Tf 5.924 1.434 Td [(is)]TJ ET 1 0 0 1 45.354 107.469 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -107.469 cm BT /F51 8.2889 Tf 45.354 97.008 Td [(a)-293(side)-292(of)-293(the)-293(quadrilateral)-292(having)]TJ/F52 8.2889 Tf 129.413 0 Td [(e)]TJ/F51 8.2889 Tf 3.978 0 Td [(2)]TJ/F191 6.6948 Tf 4.8 -1.434 Td [(\000)]TJ/F52 5.8022 Tf 5.221 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 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Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(;)]TJ/F52 8.2889 Tf 13.048 0 Td [(f)]TJ/F51 8.2889 Tf 4.165 0 Td [(0)]TJ/F52 5.8022 Tf 4.799 4.746 Td [(j)]TJ 0 -7.439 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.048 0 Td [(f)]TJ/F51 8.2889 Tf 4.165 0 Td [(1)]TJ/F52 5.8022 Tf 4.8 3.95 Td [(k)]TJ 0 -6.523 Td [(k)]TJ/F192 9.5641 Tf 3.515 2.573 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(h)]TJ/F51 8.2889 Tf 4.674 0 Td [(01)]TJ/F52 5.8022 Tf 9.599 -1.435 Td [(jk)]TJ/F191 9.5641 Tf 5.192 1.435 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(;)]TJ ET 1 0 0 1 45.354 418.707 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -418.707 cm BT /F51 8.2889 Tf 45.354 401.994 Td [(respectively.)-203(Notice)-202(that,)-203(unlike)-202(the)-202(first)-203(group,)-202(whose)-203(two)-202(pyramids)-202(share)-203(only)-202(the)-203(quadrilateral)-202(face,)]TJ 0 -10.461 Td [(these)-216(two)-216(pyramids)-215(share)-216(both)-216(the)-216(quadrilateral)-216(face)]TJ/F52 8.2889 Tf 201.333 0 Td [(q)]TJ/F51 8.2889 Tf 4.451 0 Td [(01)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(jk)]TJ/F51 8.2889 Tf 6.981 1.435 Td [(and)-216(the)-216(triangular)-215(face)]TJ/F52 8.2889 Tf 87.201 0 Td [(h)]TJ/F51 8.2889 Tf 4.675 0 Td [(01)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(jk)]TJ/F51 8.2889 Tf 5.192 1.435 Td [(.)-216(Denote)-216(these)]TJ -329.029 -11.682 Td [(pyramids)-250(by)]TJ/F52 8.2889 Tf 49.476 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(01)]TJ/F52 5.8022 Tf 0 -6.264 Td [(jk)]TJ/F51 8.2889 Tf 7.217 2.692 Td [(,)]TJ/F52 8.2889 Tf 4.012 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(10)]TJ/F52 5.8022 Tf 0 -6.264 Td [(jk)]TJ/F51 8.2889 Tf 7.217 2.692 Td [(,)-250(respectively.)-250(The)-250(list)-250(of)-250(all)-250(the)-250(6)]TJ/F52 8.2889 Tf 124.333 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F51 8.2889 Tf 5.93 -3.472 Td [(3-cells)-250(in)-250(the)-250(second)-250(group)-250(then)-250(is:)]TJ/F52 8.2889 Tf -199.745 -19.463 Td [(B)]TJ/F51 8.2889 Tf 4.767 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.95 Td [(01)]TJ/F52 5.8022 Tf 0 -6.523 Td [(jk)]TJ/F192 9.5641 Tf 7.217 2.573 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.95 Td [(10)]TJ/F52 5.8022 Tf 0 -6.523 Td [(jk)]TJ/F192 9.5641 Tf 7.217 2.573 Td [(;)]TJ/F52 8.2889 Tf -56.212 -16.187 Td [(B)]TJ/F51 8.2889 Tf 4.767 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.95 Td [(01)]TJ/F52 5.8022 Tf 0 -6.523 Td [(jk)]TJ/F192 9.5641 Tf 7.217 2.573 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.95 Td [(10)]TJ/F52 5.8022 Tf 0 -6.523 Td [(jk)]TJ/F192 9.5641 Tf 7.217 2.573 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(j)]TJ/F192 9.5641 Tf 2.395 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(k)]TJ/F191 9.5641 Tf 6.967 0 Td [(D)]TJ/F51 8.2889 Tf 10.116 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.191 0 Td [(n)]TJ/F191 9.5641 Tf 6.917 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(1)-250(\050mod)]TJ/F52 8.2889 Tf 29.326 0 Td [(n)]TJ/F51 8.2889 Tf 4.791 0 Td [(\051)]TJ/F192 9.5641 Tf 3.059 0 Td [(:)]TJ ET 1 0 0 1 410.124 344.201 cm 0 g 0 G 1 0 0 1 -410.124 -344.201 cm BT /F51 8.2889 Tf 412.196 344.201 Td [(\05017\051)]TJ ET 1 0 0 1 427.92 344.201 cm 0 g 0 G 1 0 0 1 -427.92 -344.201 cm BT /F52 8.2889 Tf 77.314 328.014 Td [(B)]TJ/F51 8.2889 Tf 4.767 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.95 Td [(01)]TJ/F52 5.8022 Tf 0 -6.522 Td [(jk)]TJ/F192 9.5641 Tf 7.217 2.572 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.95 Td [(10)]TJ/F52 5.8022 Tf 0 -6.522 Td [(jk)]TJ/F192 9.5641 Tf 7.217 2.572 Td [(:)]TJ/F51 8.2889 Tf -76.216 -19.034 Td [(We)-297(are)-297(now)-297(ready)-298(to)-297(tessellate)-297(the)]TJ/F144 8.6077 Tf 136.834 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 6.321 -3.472 Td [(by)-297(4-cells.)-298(Each)-297(4-cell)-297(is)-297(bounded)-297(by)-298(four)-297(pyramids,)-297(two)]TJ ET 1 0 0 1 45.354 308.98 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -308.98 cm BT /F51 8.2889 Tf 45.354 298.52 Td [(from)-252(each)-252(of)-252(the)-252(groups)]TJ ET 1 0 0 1 138.146 298.52 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -138.146 -298.52 cm BT /F51 8.2889 Tf 138.146 298.52 Td [(\050)]TJ ET 1 0 0 1 141.213 298.52 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -141.213 -298.52 cm BT /F51 8.2889 Tf 141.213 298.52 Td [(16)]TJ ET 1 0 0 1 150.812 298.52 cm 0 g 0 G 1 0 0 1 -150.812 -298.52 cm BT /F51 8.2889 Tf 150.812 298.52 Td [(\051)-252(and)-252(\050)]TJ ET 1 0 0 1 175.363 298.52 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -175.363 -298.52 cm BT /F51 8.2889 Tf 175.363 298.52 Td [(17)]TJ ET 1 0 0 1 184.961 298.52 cm 0 g 0 G 1 0 0 1 -184.961 -298.52 cm BT /F51 8.2889 Tf 184.961 298.52 Td [(\051;)-252(in)-252(fact,)-252(two)-252(from)-252(one)-252(determine)-252(the)-252(two)-252(from)-252(t)1(he)-252(other.)-252(Since)]TJ ET 1 0 0 1 45.354 298.52 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -298.52 cm BT /F51 8.2889 Tf 45.354 288.059 Td [(every)-309(3-cell)-308(should)-309(be)-309(the)-308(face)-309(of)-309(exactly)-308(two)-309(4-cells,)-309(it)-308(follows)-309(that)-308(there)-309(are)-309(in)-308(all)-309(6)]TJ/F52 8.2889 Tf 328.663 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F51 8.2889 Tf 6.416 -3.472 Td [(4-cells.)-309(We)]TJ ET 1 0 0 1 45.354 288.059 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -288.059 cm BT /F51 8.2889 Tf 45.354 277.598 Td [(illustrate)-250(one)-250(of)-250(them)-250(as)-250(follows.)]TJ ET 1 0 0 1 45.354 277.598 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -277.598 cm BT /F51 8.2889 Tf 57.31 266.969 Td [(Start)-440(with)]TJ/F52 8.2889 Tf 43.256 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(01)]TJ/F51 5.8022 Tf 9.599 3.52 Td [(1)]TJ/F52 5.8022 Tf 0 -6.212 Td [(jk)]TJ/F51 8.2889 Tf 8.842 2.692 Td [(in)]TJ ET 1 0 0 1 135.197 266.969 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -135.197 -266.969 cm BT /F51 8.2889 Tf 135.197 266.969 Td [(\050)]TJ ET 1 0 0 1 138.264 266.969 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -138.264 -266.969 cm BT /F51 8.2889 Tf 138.264 266.969 Td [(16)]TJ ET 1 0 0 1 147.863 266.969 cm 0 g 0 G 1 0 0 1 -147.863 -266.969 cm BT /F51 8.2889 Tf 147.863 266.969 Td [(\051.)-441(The)-441(other)-440(pyramid)-440(from)]TJ ET 1 0 0 1 256.544 266.969 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -256.544 -266.969 cm BT /F51 8.2889 Tf 256.544 266.969 Td [(\050)]TJ ET 1 0 0 1 259.611 266.969 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -259.611 -266.969 cm BT /F51 8.2889 Tf 259.611 266.969 Td [(16)]TJ ET 1 0 0 1 269.209 266.969 cm 0 g 0 G 1 0 0 1 -269.209 -266.969 cm BT /F51 8.2889 Tf 269.209 266.969 Td [(\051)-440(is)-441(either)]TJ/F52 8.2889 Tf 42.911 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(1)]TJ/F52 5.8022 Tf 0 -6.213 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F51 8.2889 Tf 7.507 2.693 Td [(or)]TJ/F52 8.2889 Tf 11.748 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(1)]TJ/F191 6.6948 Tf 0 -6.213 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F51 8.2889 Tf 2.175 2.693 Td [(,)-441(as)]TJ ET 1 0 0 1 45.354 266.969 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -266.969 cm BT /F51 8.2889 Tf 45.354 254.081 Td [(these)-356(are)-356(the)-356(only)-357(other)-356(two)-356(pyramids)-356(in)]TJ ET 1 0 0 1 209.758 254.081 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -209.758 -254.081 cm BT /F51 8.2889 Tf 209.758 254.081 Td [(\050)]TJ ET 1 0 0 1 212.824 254.081 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -212.824 -254.081 cm BT /F51 8.2889 Tf 212.824 254.081 Td [(16)]TJ ET 1 0 0 1 222.423 254.081 cm 0 g 0 G 1 0 0 1 -222.423 -254.081 cm BT /F51 8.2889 Tf 222.423 254.081 Td [(\051)-356(sharing)-356(the)-356(triangular)-357(face)]TJ/F52 8.2889 Tf 112.03 0 Td [(b)]TJ/F52 5.8022 Tf 4.501 -1.435 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F51 8.2889 Tf 6.81 1.435 Td [(with)]TJ/F52 8.2889 Tf 20.673 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(1)]TJ/F52 5.8022 Tf 0 -6.212 Td [(jk)]TJ/F51 8.2889 Tf 5.192 2.692 Td [(.)-357(If,)]TJ ET 1 0 0 1 45.354 254.081 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -254.081 cm BT /F51 8.2889 Tf 45.354 241.142 Td [(say,)-322(we)-321(pick)]TJ/F52 8.2889 Tf 49.969 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(12)]TJ/F51 5.8022 Tf 9.599 3.519 Td [(1)]TJ/F52 5.8022 Tf 0 -6.212 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.018 0 Td [(\000)]TJ/F51 5.8022 Tf 5.221 0 Td [(1)]TJ/F51 8.2889 Tf 3.858 2.693 Td [(,)-322(then)-321(it)-321(is)-322(easy)-321(to)-322(see)-321(that)-322(the)-321(two)-321(pyramids)-322(from)]TJ ET 1 0 0 1 337.095 241.142 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -337.095 -241.142 cm BT /F51 8.2889 Tf 337.095 241.142 Td [(\050)]TJ ET 1 0 0 1 340.162 241.142 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -340.162 -241.142 cm BT /F51 8.2889 Tf 340.162 241.142 Td [(17)]TJ ET 1 0 0 1 349.76 241.142 cm 0 g 0 G 1 0 0 1 -349.76 -241.142 cm BT /F51 8.2889 Tf 349.76 241.142 Td [(\051)-321(must)-322(be)]TJ/F52 8.2889 Tf 39.665 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(01)]TJ/F52 5.8022 Tf 0 -6.264 Td [(jk)]TJ/F51 8.2889 Tf 9.881 2.692 Td [(and)]TJ ET 1 0 0 1 45.354 241.142 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -241.142 cm BT /F52 8.2889 Tf 45.354 228.202 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(12)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(10)]TJ/F52 5.8022 Tf 0 -6.265 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F51 8.2889 Tf 3.857 2.693 Td [(,)-277(in)-277(order)-277(to)-277(have)-277(the)-277(quadrilateral)-277(faces)]TJ/F52 8.2889 Tf 155.465 0 Td [(q)]TJ/F51 8.2889 Tf 4.451 0 Td [(01)]TJ/F52 5.8022 Tf 9.599 -1.435 Td [(jk)]TJ/F51 8.2889 Tf 7.488 1.435 Td [(and)]TJ/F52 8.2889 Tf 16.544 0 Td [(q)]TJ/F51 8.2889 Tf 4.451 0 Td [(12)]TJ/F52 5.8022 Tf 9.599 -1.435 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F51 8.2889 Tf 6.153 1.435 Td [(shared,)-277(and)-277(for)-277(the)-277(two)-277(to)]TJ ET 1 0 0 1 45.354 228.202 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -228.202 cm BT /F51 8.2889 Tf 45.354 217.741 Td [(have)-260(the)-261(triangular)-260(face)-261(from)]TJ ET 1 0 0 1 158.654 217.741 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -158.654 -217.741 cm BT /F51 8.2889 Tf 158.654 217.741 Td [(\050)]TJ ET 1 0 0 1 161.721 217.741 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -161.721 -217.741 cm BT /F51 8.2889 Tf 161.721 217.741 Td [(14)]TJ ET 1 0 0 1 171.319 217.741 cm 0 g 0 G 1 0 0 1 -171.319 -217.741 cm BT /F51 8.2889 Tf 171.319 217.741 Td [(\051)-260(in)-261(common.)-260(Therefore)-261(this)-260(4-cell)-260(is)-261(bounded)-260(by)-260(the)-261(following)-260(four)]TJ ET 1 0 0 1 45.354 217.741 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -217.741 cm BT /F51 8.2889 Tf 45.354 207.28 Td [(pyramids:)]TJ ET 1 0 0 1 45.354 207.28 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -16.881 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -190.399 cm BT /F191 9.5641 Tf 69.265 190.399 Td [(f)]TJ/F52 8.2889 Tf 3.538 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.95 Td [(1)]TJ/F52 5.8022 Tf 0 -6.523 Td [(jk)]TJ/F192 9.5641 Tf 5.192 2.573 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(12)]TJ/F51 5.8022 Tf 9.599 3.95 Td [(1)]TJ/F52 5.8022 Tf 0 -6.523 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.221 0 Td [(k)]TJ/F191 6.6948 Tf 3.018 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.857 2.573 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.95 Td [(01)]TJ/F52 5.8022 Tf 0 -6.523 Td [(jk)]TJ/F192 9.5641 Tf 7.217 2.573 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.95 Td [(10)]TJ/F52 5.8022 Tf 0 -6.523 Td [(k)]TJ/F192 6.6948 Tf 3.018 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.221 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F191 9.5641 Tf 3.858 2.573 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(:)]TJ ET 1 0 0 1 410.124 190.399 cm 0 g 0 G 1 0 0 1 -410.124 -190.399 cm BT /F51 8.2889 Tf 412.196 190.399 Td [(\05018\051)]TJ ET 1 0 0 1 427.92 190.399 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -190.399 cm BT /F51 8.2889 Tf 57.31 173.686 Td [(As)-383(illustrated)-383(in)]TJ ET 1 0 0 1 122.801 173.686 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -122.801 -173.686 cm BT /F51 8.2889 Tf 122.801 173.686 Td [(Fig.)]TJ ET 1 0 0 1 139.122 173.686 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -139.122 -173.686 cm BT /F51 8.2889 Tf 139.122 173.686 Td [(6)]TJ ET 1 0 0 1 143.921 173.686 cm 0 g 0 G 1 0 0 1 -143.921 -173.686 cm BT /F51 8.2889 Tf 143.921 173.686 Td [(,)-383(the)-383(pyramids)-383(in)]TJ ET 1 0 0 1 214.536 173.686 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -214.536 -173.686 cm BT /F51 8.2889 Tf 214.536 173.686 Td [(\050)]TJ ET 1 0 0 1 217.603 173.686 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -217.603 -173.686 cm BT /F51 8.2889 Tf 217.603 173.686 Td [(18)]TJ ET 1 0 0 1 227.201 173.686 cm 0 g 0 G 1 0 0 1 -227.201 -173.686 cm BT /F51 8.2889 Tf 227.201 173.686 Td [(\051)-383(indeed)-383(form)-383(a)-383(tessellation)-383(for)-383(a)-383(3-sphere,)-383(at)-383(least)]TJ ET 1 0 0 1 45.354 173.686 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -173.686 cm BT /F51 8.2889 Tf 45.354 163.225 Td [(combinatorially.)]TJ ET 1 0 0 1 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PMtEy_{=<>< _.4"ɭ:C;Wt$dt0z@sZq BO *.H&"w2Μx3R=kv>Ћ>DH$T5蘷lfblXP^Af͸3*g5g?n8$&  䱢HmV5ӂ{^z5%LoAGL8u7Ϗyp]4OO!eNmb>iW]j-Ρ:hl>stream 1 0 0 1 45.354 629.9 cm 0 g 0 G 1 0 0 1 -45.354 -629.9 cm BT /F52 6.6311 Tf 127.278 629.9 Td [(A.J.)-250(Hanson,)-250(J.-P.)-250(Sha)-250(/)-250(Journal)-250(of)-250(Symbolic)-250(Computation)-250(44)-250(\0502009\051)-250(591\025605)]TJ/F51 6.6311 Tf 289.124 0 Td [(599)]TJ ET 1 0 0 1 427.92 629.9 cm 0 g 0 G 1 0 0 1 -427.92 -629.9 cm BT /F51 8.2889 Tf 45.354 609.974 Td [(in)-233(the)]TJ/F144 8.6077 Tf 23.843 0 Td [(C)]TJ/F108 8.2889 Tf 6.216 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 3.858 -3.472 Td [(,)-233(which)-232(we)-233(will)-233(denote)-233(by)]TJ/F52 8.2889 Tf 98.988 0 Td [(W)]TJ/F52 5.8022 Tf 8.131 -1.434 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.434 Td [(.)-233(It)-233(is)-232(also)-233(clear)-233(that)]TJ/F144 8.6077 Tf 74.537 0 Td [(C)]TJ/F108 8.2889 Tf 6.216 0 Td [(P)]TJ/F51 5.8022 Tf 5.198 3.472 Td [(2)]TJ/F191 9.5641 Tf 6.514 -3.472 Td [(D)]TJ/F242 9.5641 Tf 10.116 7.173 Td [(S)]TJ/F52 5.8022 Tf 8.991 -9.898 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F52 8.2889 Tf 5.109 2.725 Td [(W)]TJ/F52 5.8022 Tf 8.131 -1.434 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 5.444 1.434 Td [(and)-233(there)-232(is)-233(no)]TJ ET 1 0 0 1 45.354 609.974 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -609.974 cm BT /F51 8.2889 Tf 45.354 599.514 Td [(intersection)-250(between)-250(different)]TJ/F52 8.2889 Tf 118.191 0 Td [(W)]TJ/F52 5.8022 Tf 8.131 -1.435 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.435 Td [('s)-250(at)-250(any)-250(of)-250(their)-250(interior)-250(points.)]TJ ET 1 0 0 1 45.354 599.514 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -599.514 cm BT /F51 8.2889 Tf 57.31 589.105 Td [(For)-493(clarity)-493(and)-493(later)-493(convenience,)-493(we)-493(write)-493(down)-494(the)-493(following)-493(explicit)-493(parametrization)-493(for)]TJ ET 1 0 0 1 45.354 589.105 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -589.105 cm BT /F52 8.2889 Tf 45.354 578.644 Td [(W)]TJ/F52 5.8022 Tf 8.132 -1.434 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 3.516 1.434 Td [(:)]TJ ET 1 0 0 1 45.354 578.644 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -16.905 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -561.739 cm BT /F191 9.5641 Tf 69.265 561.739 Td [(T)]TJ/F51 8.2889 Tf 3.185 0 Td [(cos)]TJ/F52 8.2889 Tf 13.96 0 Td [(s)]TJ/F51 8.2889 Tf 4.976 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(\014)]TJ/F192 9.5641 Tf 4.743 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(cos)]TJ/F52 8.2889 Tf 13.961 0 Td [(r)]TJ/F51 8.2889 Tf 5.635 0 Td [(sin)]TJ/F52 8.2889 Tf 12.8 0 Td [(s)]TJ/F192 9.5641 Tf 3.382 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(sin)]TJ/F52 8.2889 Tf 12.801 0 Td [(r)]TJ/F51 8.2889 Tf 5.634 0 Td [(sin)]TJ/F52 8.2889 Tf 12.801 0 Td [(s)]TJ/F51 8.2889 Tf 4.976 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.74 0 Td [(\013)]TJ/F191 9.5641 Tf 4.589 -3.95 Td [(U)]TJ ET 1 0 0 1 410.124 561.739 cm 0 g 0 G 1 0 0 1 -410.124 -561.739 cm BT /F51 8.2889 Tf 412.196 561.739 Td [(\05020\051)]TJ ET 1 0 0 1 427.92 561.739 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -561.739 cm BT /F51 8.2889 Tf 45.354 546.381 Td [(with)-499(0)]TJ/F191 9.5641 Tf 29.316 0 Td [(\024)]TJ/F52 8.2889 Tf 9.868 0 Td [(r)]TJ/F192 9.5641 Tf 4.041 0 Td [(;)]TJ/F52 8.2889 Tf 4.759 0 Td [(s)]TJ/F191 9.5641 Tf 6.039 0 Td [(\024)]TJ/F192 9.5641 Tf 9.868 0 Td [(\031)-100(=)]TJ/F51 8.2889 Tf 11.19 0 Td [(2,)]TJ/F192 9.5641 Tf 10.877 0 Td [(.)]TJ/F51 8.2889 Tf 3.567 0 Td [(2)]TJ/F52 8.2889 Tf 4.8 0 Td [(j)]TJ/F191 9.5641 Tf 4.511 0 Td [(\000)]TJ/F51 8.2889 Tf 9.575 0 Td [(1)]TJ/F192 9.5641 Tf 4.8 0 Td [(/\031)-100(=)]TJ/F52 8.2889 Tf 14.757 0 Td [(n)]TJ/F191 9.5641 Tf 7.448 0 Td [(\024)]TJ/F192 9.5641 Tf 9.868 0 Td [(\013)]TJ/F191 9.5641 Tf 8.5 0 Td [(\024)]TJ/F192 9.5641 Tf 9.868 0 Td [(.)]TJ/F51 8.2889 Tf 3.567 0 Td [(2)]TJ/F52 8.2889 Tf 4.8 0 Td [(j)]TJ/F191 9.5641 Tf 4.511 0 Td [(C)]TJ/F51 8.2889 Tf 9.575 0 Td [(1)]TJ/F192 9.5641 Tf 4.8 0 Td [(/\031)-100(=)]TJ/F52 8.2889 Tf 14.757 0 Td [(n)]TJ/F51 8.2889 Tf 8.929 0 Td [(and,)-250(if)-249(we)-250(denote)-499(arg)]TJ/F192 9.5641 Tf 81.911 0 Td [(.)]TJ/F191 9.5641 Tf 3.568 0 Td [(\000)]TJ/F51 8.2889 Tf 9.054 0 Td [(cos)]TJ/F52 5.8022 Tf 12.367 3.472 Td [(n)]TJ/F52 8.2889 Tf 5.445 -3.472 Td [(r)]TJ/F191 9.5641 Tf 6.157 0 Td [(\000)]TJ/F51 8.2889 Tf 9.575 0 Td [(sin)]TJ/F52 5.8022 Tf 11.207 3.777 Td [(n)]TJ/F52 8.2889 Tf 5.446 -3.777 Td [(r)]TJ/F51 8.2889 Tf 5.635 0 Td [(e)]TJ/F51 5.8022 Tf 4.359 3.472 Td [(i)]TJ/F52 5.8022 Tf 1.741 0 Td [(n)]TJ/F192 6.6948 Tf 3.354 0 Td [(\013)]TJ/F192 9.5641 Tf 4.588 -3.472 Td [(/)]TJ/F51 8.2889 Tf -378.998 -10.461 Td [(by)]TJ/F52 8.2889 Tf 11.414 0 Td [(a)]TJ/F192 9.5641 Tf 4.418 0 Td [(.)]TJ/F52 8.2889 Tf 3.567 0 Td [(r)]TJ/F192 9.5641 Tf 4.041 0 Td [(;)-167(\013)-40(/)]TJ/F51 8.2889 Tf 16.243 0 Td [(with)-250(0)]TJ/F191 9.5641 Tf 27.25 0 Td [(\024)]TJ/F52 8.2889 Tf 9.868 0 Td [(a)]TJ/F192 9.5641 Tf 4.418 0 Td [(.)]TJ/F52 8.2889 Tf 3.567 0 Td [(r)]TJ/F192 9.5641 Tf 4.041 0 Td [(;)-167(\013)-40(/)]TJ/F191 9.5641 Tf 16.827 0 Td [(\024)]TJ/F51 8.2889 Tf 9.868 0 Td [(2)]TJ/F192 9.5641 Tf 4.8 0 Td [(\031)]TJ/F51 8.2889 Tf 6.695 0 Td [(,)-250(then)]TJ/F52 8.2889 Tf -101.911 -15.083 Td [(a)]TJ/F192 9.5641 Tf 4.418 0 Td [(.)]TJ/F52 8.2889 Tf 3.568 0 Td [(r)]TJ/F192 9.5641 Tf 4.04 0 Td [(;)-167(\013)-40(/)]TJ/F191 9.5641 Tf 16.296 0 Td [(C)]TJ/F51 8.2889 Tf 9.586 0 Td [(2)]TJ/F192 9.5641 Tf 4.799 0 Td [(.)]TJ/F52 8.2889 Tf 3.567 0 Td [(j)]TJ/F191 9.5641 Tf 4.521 0 Td [(C)]TJ/F52 8.2889 Tf 9.586 0 Td [(k)]TJ/F191 9.5641 Tf 6.435 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(1)]TJ/F192 9.5641 Tf 4.8 0 Td [(/\031)]TJ ET q 1 0 0 1 70.46 516.524 cm []0 d 0 J 0.44 w 0 0 m 91.463 0 l S Q BT /F52 8.2889 Tf 113.796 507.343 Td [(n)]TJ/F191 9.5641 Tf 51.979 6.79 Td [(\024)]TJ/F192 9.5641 Tf 9.868 0 Td [(\014)]TJ/F191 9.5641 Tf 8.72 0 Td [(\024)]TJ/F52 8.2889 Tf 11.064 6.704 Td [(a)]TJ/F192 9.5641 Tf 4.418 0 Td [(.)]TJ/F52 8.2889 Tf 3.567 0 Td [(r)]TJ/F192 9.5641 Tf 4.041 0 Td [(;)-167(\013)-40(/)]TJ/F191 9.5641 Tf 16.296 0 Td [(C)]TJ/F51 8.2889 Tf 9.585 0 Td [(2)]TJ/F192 9.5641 Tf 4.8 0 Td [(.)]TJ/F52 8.2889 Tf 3.567 0 Td [(j)]TJ/F191 9.5641 Tf 4.521 0 Td [(C)]TJ/F52 8.2889 Tf 9.585 0 Td [(k)]TJ/F192 9.5641 Tf 4.31 0 Td [(/\031)]TJ ET q 1 0 0 1 195.427 516.524 cm []0 d 0 J 0.44 w 0 0 m 74.953 0 l S Q BT /F52 8.2889 Tf 230.508 507.343 Td [(n)]TJ/F192 9.5641 Tf 41.067 6.79 Td [(:)]TJ/F51 8.2889 Tf -226.221 -19.99 Td [(We)-250(see)-250(in)-250(particular)-250(that)]TJ/F192 9.5641 Tf 96.134 0 Td [(w)]TJ/F51 8.2889 Tf 7.317 0 Td [(1)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(p)]TJ/F51 5.8022 Tf 3.226 0 Td [(20)]TJ/F191 9.5641 Tf 9.874 1.435 Td [(D)]TJ/F192 9.5641 Tf 10.117 0 Td [(w)]TJ/F51 8.2889 Tf 7.316 0 Td [(2)]TJ/F191 6.6948 Tf 4.799 -1.435 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.435 Td [(.)-250(See)]TJ ET 1 0 0 1 228.977 494.143 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -228.977 -494.143 cm BT /F51 8.2889 Tf 228.977 494.143 Td [(Fig.)]TJ ET 1 0 0 1 244.196 494.143 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -244.196 -494.143 cm BT /F51 8.2889 Tf 244.196 494.143 Td [(8)]TJ ET 1 0 0 1 248.995 494.143 cm 0 g 0 G 1 0 0 1 -248.995 -494.143 cm BT /F51 8.2889 Tf 248.995 494.143 Td [(.)]TJ ET 1 0 0 1 45.354 494.143 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -494.143 cm BT /F51 8.2889 Tf 57.31 483.734 Td [(From)]TJ ET 1 0 0 1 79.464 483.734 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -79.464 -483.734 cm BT /F51 8.2889 Tf 79.464 483.734 Td [(\050)]TJ ET 1 0 0 1 82.531 483.734 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -82.531 -483.734 cm BT /F51 8.2889 Tf 82.531 483.734 Td [(20)]TJ ET 1 0 0 1 92.129 483.734 cm 0 g 0 G 1 0 0 1 -92.129 -483.734 cm BT /F51 8.2889 Tf 92.129 483.734 Td [(\051,)-260(it)-260(follows)-259(that,)-260(in)-260(a)-260(way)-260(similar)-260(to)-259(the)-260(above,)]TJ/F52 8.2889 Tf 178.774 0 Td [(W)]TJ/F52 5.8022 Tf 8.132 -1.434 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 5.669 1.434 Td [(can)-260(also)-260(be)-259(described)-260(as)-260(a)-260(union)]TJ ET 1 0 0 1 45.354 483.734 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -483.734 cm BT /F51 8.2889 Tf 45.354 473.274 Td [(of)]TJ/F192 9.5641 Tf 9.58 0 Td [(w)]TJ/F51 8.2889 Tf 7.316 0 Td [(2)]TJ/F191 6.6948 Tf 4.8 -1.435 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(p)]TJ/F51 8.2889 Tf 5.844 1.435 Td [(over)]TJ/F52 8.2889 Tf 19.07 0 Td [(p)]TJ/F191 9.5641 Tf 7.387 0 Td [(2)]TJ/F192 9.5641 Tf 8.794 0 Td [(w)]TJ/F51 8.2889 Tf 7.317 0 Td [(1)]TJ/F52 5.8022 Tf 4.799 -1.435 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.435 Td [(,)-256(or)-255(a)-256(union)-256(of)]TJ/F192 9.5641 Tf 54.604 0 Td [(w)]TJ/F51 8.2889 Tf 7.316 0 Td [(0)]TJ/F52 5.8022 Tf 4.8 -1.435 Td [(j)]TJ/F192 6.6948 Tf 1.676 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(p)]TJ/F51 8.2889 Tf 5.844 1.435 Td [(over)]TJ/F52 8.2889 Tf 19.07 0 Td [(p)]TJ/F191 9.5641 Tf 7.387 0 Td [(2)]TJ/F192 9.5641 Tf 8.794 0 Td [(w)]TJ/F51 8.2889 Tf 7.317 0 Td [(2)]TJ/F191 6.6948 Tf 4.799 -1.435 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.435 Td [(.)-256(Therefore)-255(the)-256(boundary)-256(of)]TJ/F52 8.2889 Tf 106.135 0 Td [(W)]TJ/F52 5.8022 Tf 8.132 -1.435 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.215 0 Td [(k)]TJ/F192 6.6948 Tf 3.018 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 5.635 1.435 Td [(is)]TJ ET 1 0 0 1 45.354 473.274 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -473.274 cm BT /F51 8.2889 Tf 45.354 462.813 Td [(tessellated)-211(by)-211(twelve)-212(3-cells;)-211(each)-211(of)-211(them)-212(is)-211(the)-211(union)-211(of)-211(one)-212(of)-211(the)-211(two)-211(lower)-211(half)-212(boundary)-211(edges)-211(of)]TJ ET 1 0 0 1 45.354 462.813 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -462.813 cm BT /F51 8.2889 Tf 45.354 452.352 Td [(a)]TJ/F192 9.5641 Tf 6.411 0 Td [(w)]TJ/F51 8.2889 Tf 7.317 0 Td [(-region)-255(over)-256(one)-255(of)-256(the)-255(two)-256(triangles)-255(in)-255(the)-256(corresponding)-255(base)-256(region.)-255(It)-256(is)-255(easy)-256(to)-255(see)-255(that)-256(these)]TJ ET 1 0 0 1 45.354 452.352 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -452.352 cm BT /F51 8.2889 Tf 45.354 441.891 Td [(3-cells)-250(are)-250(in)-250(fact)-250(exactly)-250(the)-250(following)-250(twelve)-250(pyramids)-250(in)]TJ ET 1 0 0 1 270.396 441.891 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -270.396 -441.891 cm BT /F51 8.2889 Tf 270.396 441.891 Td [(\050)]TJ ET 1 0 0 1 273.463 441.891 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -273.463 -441.891 cm BT /F51 8.2889 Tf 273.463 441.891 Td [(16)]TJ ET 1 0 0 1 283.062 441.891 cm 0 g 0 G 1 0 0 1 -283.062 -441.891 cm BT /F51 8.2889 Tf 283.062 441.891 Td [(\051:)]TJ ET 1 0 0 1 45.354 441.891 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -30.637 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -411.254 cm BT /F52 8.2889 Tf 69.265 426.329 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(1)]TJ/F52 5.8022 Tf 0 -6.213 Td [(k)]TJ/F191 6.6948 Tf 3.018 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 9.5641 Tf 3.515 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.128 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(2)]TJ/F52 5.8022 Tf 0 -6.213 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 9.5641 Tf 3.516 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.128 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(12)]TJ/F51 5.8022 Tf 9.599 3.52 Td [(1)]TJ/F52 5.8022 Tf 0 -6.213 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.857 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.129 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(2)]TJ/F52 5.8022 Tf 0 -6.213 Td [(k)]TJ/F192 6.6948 Tf 3.018 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(;)]TJ/F52 8.2889 Tf -215.706 -14.71 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(20)]TJ/F51 5.8022 Tf 9.599 3.519 Td [(1)]TJ/F191 6.6948 Tf 0 -6.212 Td [(\000)]TJ/F52 5.8022 Tf 5.221 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F192 9.5641 Tf 2.175 2.693 Td [(;)]TJ/F52 8.2889 Tf 14.468 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.519 Td [(2)]TJ/F191 6.6948 Tf 0 -6.212 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F192 9.5641 Tf 2.175 2.693 Td [(;)]TJ/F52 8.2889 Tf 14.469 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(20)]TJ/F51 5.8022 Tf 9.599 3.519 Td [(1)]TJ/F191 6.6948 Tf 0 -6.212 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.221 0 Td [(k)]TJ/F192 6.6948 Tf 3.018 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(;)]TJ/F52 8.2889 Tf 14.469 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.519 Td [(2)]TJ/F191 6.6948 Tf 0 -6.212 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(;)]TJ/F52 8.2889 Tf -214.366 -14.711 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.519 Td [(1)]TJ/F52 5.8022 Tf 0 -6.212 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 9.5641 Tf 3.515 2.693 Td [(;)]TJ/F52 8.2889 Tf 26.589 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.519 Td [(2)]TJ/F52 5.8022 Tf 0 -6.212 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 9.5641 Tf 3.515 2.693 Td [(;)]TJ/F52 8.2889 Tf 26.59 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(01)]TJ/F51 5.8022 Tf 9.599 3.519 Td [(1)]TJ/F52 5.8022 Tf 0 -6.212 Td [(j)]TJ/F192 6.6948 Tf 1.676 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F191 6.6948 Tf 3.018 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.857 2.693 Td [(;)]TJ/F52 8.2889 Tf 26.589 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.519 Td [(2)]TJ/F52 5.8022 Tf 0 -6.212 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(:)]TJ ET 1 0 0 1 410.124 411.254 cm 0 g 0 G 1 0 0 1 -410.124 -411.254 cm BT /F51 8.2889 Tf 412.196 411.254 Td [(\05021\051)]TJ ET 1 0 0 1 427.92 411.254 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -411.254 cm BT /F51 8.2889 Tf 57.31 380.734 Td [(It)-304(is)-305(also)-305(easy)-304(to)-305(see)-304(there)-305(are)-304(six)-305(3-cells)-304(contained)-305(inside)]TJ/F52 8.2889 Tf 223.53 0 Td [(W)]TJ/F52 5.8022 Tf 8.131 -1.435 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 3.515 1.435 Td [(;)-305(each)-304(of)-305(them)-304(is)-305(the)-304(union)-305(of)]TJ ET 1 0 0 1 45.354 380.734 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -380.734 cm BT /F51 8.2889 Tf 45.354 370.273 Td [(one)-271(of)-271(the)-271(two)-271(triangles)-271(in)-271(a)]TJ/F192 9.5641 Tf 109.779 0 Td [(w)]TJ/F51 8.2889 Tf 7.317 0 Td [(-region)-271(over)-271(the)-271(middle)-271(edge)-271(of)-271(the)-271(corresponding)-271(base)-271(region.)-271(These)]TJ ET 1 0 0 1 45.354 370.273 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -370.273 cm BT /F51 8.2889 Tf 45.354 359.812 Td [(3-cells)-250(are)-250(the)-250(following)-250(six)-250(pyramids)-250(in)]TJ ET 1 0 0 1 200.099 359.812 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -200.099 -359.812 cm BT /F51 8.2889 Tf 200.099 359.812 Td [(\050)]TJ ET 1 0 0 1 203.166 359.812 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -203.166 -359.812 cm BT /F51 8.2889 Tf 203.166 359.812 Td [(17)]TJ ET 1 0 0 1 212.764 359.812 cm 0 g 0 G 1 0 0 1 -212.764 -359.812 cm BT /F51 8.2889 Tf 212.764 359.812 Td [(\051:)]TJ ET 1 0 0 1 45.354 359.812 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -30.716 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -329.096 cm BT /F52 8.2889 Tf 69.265 344.198 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(10)]TJ/F52 5.8022 Tf 0 -6.265 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.221 0 Td [(k)]TJ/F192 9.5641 Tf 3.516 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.128 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(12)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(01)]TJ/F52 5.8022 Tf 0 -6.265 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F52 8.2889 Tf -96.901 -12.07 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(10)]TJ/F191 6.6948 Tf 0 -6.265 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F192 9.5641 Tf 2.174 2.693 Td [(;)]TJ/F52 8.2889 Tf 14.469 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(20)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(01)]TJ/F191 6.6948 Tf 0 -6.265 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(;)]TJ/F52 8.2889 Tf -99.418 -14.763 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(10)]TJ/F52 5.8022 Tf 0 -6.265 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 9.5641 Tf 3.516 2.693 Td [(;)]TJ/F52 8.2889 Tf 26.589 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(01)]TJ/F52 5.8022 Tf 0 -6.265 Td [(j)]TJ/F192 6.6948 Tf 1.676 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(:)]TJ ET 1 0 0 1 410.124 329.096 cm 0 g 0 G 1 0 0 1 -410.124 -329.096 cm BT /F51 8.2889 Tf 412.196 329.096 Td [(\05022\051)]TJ ET 1 0 0 1 427.92 329.096 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -329.096 cm BT /F51 8.2889 Tf 45.354 298.498 Td [(These)-250(3-cells)-250(divide)]TJ/F52 8.2889 Tf 77.161 0 Td [(W)]TJ/F52 5.8022 Tf 8.131 -1.435 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F51 8.2889 Tf 5.588 1.435 Td [(into)-250(six)-250(4-cells;)-250(they)-250(are)-250(the)-250(following)-250(six)-250(in)]TJ ET 1 0 0 1 326.399 298.498 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -326.399 -298.498 cm BT /F51 8.2889 Tf 326.399 298.498 Td [(\050)]TJ ET 1 0 0 1 329.466 298.498 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -329.466 -298.498 cm BT /F51 8.2889 Tf 329.466 298.498 Td [(19)]TJ ET 1 0 0 1 339.064 298.498 cm 0 g 0 G 1 0 0 1 -339.064 -298.498 cm BT /F51 8.2889 Tf 339.064 298.498 Td [(\051:)]TJ ET 1 0 0 1 45.354 298.498 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -53.773 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -244.725 cm BT /F191 9.5641 Tf 69.265 281.971 Td [(f)]TJ/F52 8.2889 Tf 3.538 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(1)]TJ/F52 5.8022 Tf 0 -6.213 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(;)]TJ/F52 8.2889 Tf 26.589 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(12)]TJ/F51 5.8022 Tf 9.599 3.52 Td [(1)]TJ/F52 5.8022 Tf 0 -6.213 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 9.5641 Tf 3.515 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.129 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(01)]TJ/F52 5.8022 Tf 0 -6.265 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(;)]TJ/F52 8.2889 Tf 28.661 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(12)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(10)]TJ/F52 5.8022 Tf 0 -6.265 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 9.5641 Tf 3.515 2.693 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(;)]TJ/F191 9.5641 Tf -224.325 -14.763 Td [(f)]TJ/F52 8.2889 Tf 3.538 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(2)]TJ/F52 5.8022 Tf 0 -6.213 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 9.5641 Tf 3.516 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.128 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(20)]TJ/F51 5.8022 Tf 9.599 3.52 Td [(2)]TJ/F191 6.6948 Tf 0 -6.213 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.221 0 Td [(k)]TJ/F192 6.6948 Tf 3.018 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(;)]TJ/F52 8.2889 Tf 14.469 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(10)]TJ/F52 5.8022 Tf 0 -6.265 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.36 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 9.5641 Tf 5.588 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.128 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(20)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(01)]TJ/F191 6.6948 Tf 0 -6.265 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.221 0 Td [(k)]TJ/F192 6.6948 Tf 3.018 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F191 6.6948 Tf 1.676 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F191 9.5641 Tf 3.858 2.693 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(;)]TJ/F191 9.5641 Tf -222.985 -14.763 Td [(f)]TJ/F52 8.2889 Tf 3.538 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(1)]TJ/F191 6.6948 Tf 0 -6.213 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.857 2.693 Td [(;)]TJ/F52 8.2889 Tf 14.469 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(01)]TJ/F51 5.8022 Tf 9.599 3.52 Td [(1)]TJ/F52 5.8022 Tf 0 -6.213 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 9.5641 Tf 3.515 2.693 Td [(;)]TJ/F52 8.2889 Tf 26.59 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(01)]TJ/F191 6.6948 Tf 0 -6.265 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.857 2.693 Td [(;)]TJ/F52 8.2889 Tf 16.541 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(10)]TJ/F52 5.8022 Tf 0 -6.265 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F191 9.5641 Tf 3.515 2.693 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(;)]TJ/F191 9.5641 Tf -210.864 -14.763 Td [(f)]TJ/F52 8.2889 Tf 3.538 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(2)]TJ/F52 5.8022 Tf 0 -6.213 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 9.5641 Tf 3.516 2.693 Td [(;)]TJ/F52 8.2889 Tf 26.589 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(12)]TJ/F51 5.8022 Tf 9.599 3.52 Td [(2)]TJ/F52 5.8022 Tf 0 -6.213 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.857 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.129 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(10)]TJ/F52 5.8022 Tf 0 -6.265 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F192 9.5641 Tf 3.516 2.693 Td [(;)]TJ/F52 8.2889 Tf 28.661 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(12)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(01)]TJ/F52 5.8022 Tf 0 -6.265 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F191 9.5641 Tf 3.857 2.693 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(;)]TJ/F191 9.5641 Tf -224.325 -14.763 Td [(f)]TJ/F52 8.2889 Tf 3.538 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(1)]TJ/F52 5.8022 Tf 0 -6.213 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.858 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.128 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(20)]TJ/F51 5.8022 Tf 9.599 3.52 Td [(1)]TJ/F191 6.6948 Tf 0 -6.213 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F192 9.5641 Tf 2.175 2.693 Td [(;)]TJ/F52 8.2889 Tf 14.469 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(12)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(01)]TJ/F52 5.8022 Tf 0 -6.265 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(;)]TJ/F191 6.6948 Tf 2.216 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 5.93 2.693 Td [(;)]TJ/F52 8.2889 Tf 13.128 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(20)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(10)]TJ/F191 6.6948 Tf 0 -6.265 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F191 9.5641 Tf 2.175 2.693 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(;)]TJ/F191 9.5641 Tf -222.985 -14.763 Td [(f)]TJ/F52 8.2889 Tf 3.538 0 Td [(A)]TJ/F51 8.2889 Tf 5.032 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.52 Td [(2)]TJ/F191 6.6948 Tf 0 -6.213 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F192 9.5641 Tf 2.175 2.693 Td [(;)]TJ/F52 8.2889 Tf 14.469 0 Td [(A)]TJ/F51 8.2889 Tf 5.031 0 Td [(01)]TJ/F51 5.8022 Tf 9.599 3.52 Td [(2)]TJ/F52 5.8022 Tf 0 -6.213 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 9.5641 Tf 3.857 2.693 Td [(;)]TJ/F52 8.2889 Tf 26.59 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(20)]TJ/F51 5.8022 Tf 9.598 3.572 Td [(10)]TJ/F191 6.6948 Tf 0 -6.265 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(j)]TJ/F191 6.6948 Tf 1.677 0 Td [(\000)]TJ/F52 5.8022 Tf 5.222 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F192 6.6948 Tf 3.359 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(j)]TJ/F192 9.5641 Tf 2.175 2.693 Td [(;)]TJ/F52 8.2889 Tf 16.541 0 Td [(B)]TJ/F51 8.2889 Tf 4.766 0 Td [(01)]TJ/F51 5.8022 Tf 9.599 3.572 Td [(01)]TJ/F52 5.8022 Tf 0 -6.265 Td [(j)]TJ/F192 6.6948 Tf 1.677 0 Td [(;)]TJ/F52 5.8022 Tf 2.216 0 Td [(k)]TJ/F191 6.6948 Tf 3.017 0 Td [(\000)]TJ/F51 5.8022 Tf 5.222 0 Td [(1)]TJ/F191 9.5641 Tf 3.857 2.693 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(:)]TJ ET 1 0 0 1 410.124 244.725 cm 0 g 0 G 1 0 0 1 -410.124 -244.725 cm BT /F51 8.2889 Tf 412.196 244.725 Td [(\05023\051)]TJ ET 1 0 0 1 427.92 244.725 cm 0 g 0 G 1 0 0 1 -382.566 0 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -244.725 cm BT /F51 8.2889 Tf 57.31 191.982 Td [(The)-250(structure)-250(of)]TJ ET 1 0 0 1 119.965 191.982 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -119.965 -191.982 cm BT /F51 8.2889 Tf 119.965 191.982 Td [(\050)]TJ ET 1 0 0 1 123.032 191.982 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -123.032 -191.982 cm BT /F51 8.2889 Tf 123.032 191.982 Td [(21)]TJ ET 1 0 0 1 132.63 191.982 cm 0 g 0 G 1 0 0 1 -132.63 -191.982 cm BT /F51 8.2889 Tf 132.63 191.982 Td [(\051\025\050)]TJ ET 1 0 0 1 143.555 191.982 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -143.555 -191.982 cm BT /F51 8.2889 Tf 143.555 191.982 Td [(23)]TJ ET 1 0 0 1 153.153 191.982 cm 0 g 0 G 1 0 0 1 -153.153 -191.982 cm BT /F51 8.2889 Tf 153.153 191.982 Td [(\051)-250(together)-250(can)-250(be)-250(illustrated)-250(by)-250(the)-250(diagram)-250(in)]TJ ET 1 0 0 1 330.021 191.982 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -330.021 -191.982 cm BT /F51 8.2889 Tf 330.021 191.982 Td [(Fig.)]TJ ET 1 0 0 1 345.239 191.982 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -345.239 -191.982 cm BT /F51 8.2889 Tf 345.239 191.982 Td [(9)]TJ ET 1 0 0 1 350.038 191.982 cm 0 g 0 G 1 0 0 1 -350.038 -191.982 cm BT /F51 8.2889 Tf 350.038 191.982 Td [(.)]TJ ET 1 0 0 1 45.354 191.982 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -191.982 cm BT /F51 8.2889 Tf 57.31 181.573 Td [(Now)-250(it)-250(is)-250(clear)-250(that)-250(the)]TJ/F144 8.6077 Tf 88.599 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 5.93 -3.472 Td [(is)-250(well)-250(tessellated.)]TJ ET 1 0 0 1 45.354 181.573 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -181.573 cm BT /F108 8.2889 Tf 57.31 171.165 Td [(Remark.)]TJ/F51 8.2889 Tf 35.523 0 Td [(If)-221(all)-220(we)-221(need)-220(is)-221(a)-220(tessellation)-221(of)-220(the)]TJ/F144 8.6077 Tf 135.355 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 5.685 -3.472 Td [(\050and)-221(hence)]TJ/F52 8.2889 Tf 43.708 0 Td [(F)]TJ/F52 5.8022 Tf 4.028 -1.435 Td [(n)]TJ/F51 8.2889 Tf 3.852 1.435 Td [(\051,)-221(then)-220(the)-221(triangles)-220(in)]TJ ET 1 0 0 1 381.817 171.165 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 1 0 0 1 -381.817 -171.165 cm BT /F51 8.2889 Tf 381.817 171.165 Td [(\050)]TJ ET 1 0 0 1 384.884 171.165 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -384.884 -171.165 cm BT /F51 8.2889 Tf 384.884 171.165 Td [(14)]TJ ET 1 0 0 1 394.482 171.165 cm 0 g 0 G 1 0 0 1 -394.482 -171.165 cm BT /F51 8.2889 Tf 394.482 171.165 Td [(\051)-221(and)-220(the)]TJ ET 1 0 0 1 45.354 171.165 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -171.165 cm BT /F51 8.2889 Tf 45.354 160.704 Td [(3-cells)-283(in)]TJ ET 1 0 0 1 82.743 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8.2889 Tf 283.197 293.113 Td [(\051)-220(which)-220(is)-219(induced)-220(from)-220(the)-220(projection)]TJ ET 1 0 0 1 45.354 293.113 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -293.113 cm BT /F191 9.5641 Tf 45.354 282.652 Td [(T)]TJ/F52 8.2889 Tf 3.185 0 Td [(z)]TJ/F51 5.8022 Tf 3.714 -1.435 Td [(0)]TJ/F192 9.5641 Tf 3.857 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(1)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(2)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.759 0 Td [(z)]TJ/F51 5.8022 Tf 3.714 -1.435 Td [(3)]TJ/F191 9.5641 Tf 3.857 1.435 Td [(U)-618(7)1(!)-617(T)]TJ/F52 8.2889 Tf 28.694 0 Td [(z)]TJ/F51 5.8022 Tf 3.714 -1.435 Td [(0)]TJ/F192 9.5641 Tf 3.857 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(1)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(2)]TJ/F191 9.5641 Tf 3.857 1.435 Td [(U)]TJ/F51 8.2889 Tf 3.185 0 Td [(,)-403(we)-403(use)-403(the)-403(branched)-403(covering)-403(induced)-403(from,)-403(say,)]TJ/F191 9.5641 Tf 203.356 0 Td [(T)]TJ/F52 8.2889 Tf 3.185 0 Td [(z)]TJ/F51 5.8022 Tf 3.714 -1.435 Td [(0)]TJ/F192 9.5641 Tf 3.857 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(1)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(2)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(;)]TJ/F52 8.2889 Tf 4.759 0 Td [(z)]TJ/F51 5.8022 Tf 3.714 -1.435 Td [(3)]TJ/F191 9.5641 Tf 3.857 1.435 Td [(U)-618(7)1(!)]TJ ET 1 0 0 1 45.354 282.652 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -282.652 cm BT /F191 9.5641 Tf 45.354 272.191 Td [(T)]TJ/F52 8.2889 Tf 3.185 0 Td [(z)]TJ/F51 5.8022 Tf 3.714 -1.434 Td [(1)]TJ/F192 9.5641 Tf 3.857 1.434 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.434 Td [(2)]TJ/F192 9.5641 Tf 3.858 1.434 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.434 Td [(3)]TJ/F191 9.5641 Tf 3.858 1.434 Td [(U)]TJ/F51 8.2889 Tf 3.184 0 Td [(,)-543(the)-542(lifted)-543(tessellation)-543(will)-542(be)-543(the)-542(same.)-545(This,)-542(combined)-543(with)-543(the)-542(invariance)-543(for)]TJ/F52 8.2889 Tf 336.05 0 Td [(S)]TJ/F52 5.8022 Tf 4.062 -1.434 Td [(n)]TJ ET 1 0 0 1 45.354 272.191 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -272.191 cm BT /F51 8.2889 Tf 45.354 261.731 Td [(demonstrated)-239(in)-240(Section)]TJ ET 1 0 0 1 140.37 261.731 cm 0 0 .4 rg 0 0 .4 RG 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -140.37 -261.731 cm BT /F51 8.2889 Tf 140.37 261.731 Td [(1)]TJ ET 1 0 0 1 145.169 261.731 cm 0 g 0 G 1 0 0 1 -145.169 -261.731 cm BT /F51 8.2889 Tf 145.169 261.731 Td [(,)-239(shows)-240(that)-239(the)-239(tessellation)-240(of)-239(the)]TJ/F52 8.2889 Tf 131.731 0 Td [(F)]TJ/F52 5.8022 Tf 4.029 -1.435 Td [(n)]TJ/F51 8.2889 Tf 5.836 1.435 Td [(is)]TJ/F192 9.2055 Tf 8.167 0 Td [(\000)]TJ/F52 5.8022 Tf 5.726 -1.435 Td [(n)]TJ/F51 8.2889 Tf 3.852 1.435 Td [(-invariant)-239(and)-240(the)-239(action)-239(of)]TJ/F192 9.2055 Tf 105.665 0 Td [(\000)]TJ/F52 5.8022 Tf 5.725 -1.435 Td [(n)]TJ/F51 8.2889 Tf 5.836 1.435 Td [(is)]TJ ET 1 0 0 1 45.354 261.731 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -261.731 cm BT /F51 8.2889 Tf 45.354 251.27 Td [(transitive)-250(on)-250(the)-250(set)-250(of)-250(4-cells.)]TJ ET 1 0 0 1 45.354 251.27 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -251.27 cm BT /F51 8.2889 Tf 57.31 240.715 Td [(The)-250(list)-250(of)-250(all)-250(the)-250(vertices)-250(in)-250(the)-250(tessellation)-250(is:)]TJ/F52 8.2889 Tf 11.955 -16.532 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(01)]TJ/F52 5.8022 Tf 9.599 -1.435 Td [(k)]TJ/F191 9.5641 Tf 6.172 1.435 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.931 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.\031)]TJ/F191 6.6948 Tf 7.183 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(2)]TJ/F52 5.8022 Tf 3.36 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(/=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F191 9.5641 Tf 3.852 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.184 0 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(02)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(k)]TJ/F191 9.5641 Tf 6.172 1.435 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.932 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.\031)]TJ/F191 6.6948 Tf 7.183 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(2)]TJ/F52 5.8022 Tf 3.36 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(/=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F191 9.5641 Tf 3.852 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F52 8.2889 Tf -227.522 -13.45 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(03)]TJ/F52 5.8022 Tf 9.599 -1.434 Td [(k)]TJ/F191 9.5641 Tf 6.172 1.434 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.931 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.\031)]TJ/F191 6.6948 Tf 7.183 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(2)]TJ/F52 5.8022 Tf 3.36 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(/=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(0)]TJ/F191 9.5641 Tf 4.799 0 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(12)]TJ/F52 5.8022 Tf 9.598 -1.434 Td [(k)]TJ/F191 9.5641 Tf 6.172 1.434 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.932 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.\031)]TJ/F191 6.6948 Tf 7.183 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(2)]TJ/F52 5.8022 Tf 3.36 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(/=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F191 9.5641 Tf 3.852 -3.95 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F52 8.2889 Tf -227.522 -13.449 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(13)]TJ/F52 5.8022 Tf 9.599 -1.435 Td [(k)]TJ/F191 9.5641 Tf 6.172 1.435 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.931 0 Td [(1)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.\031)]TJ/F191 6.6948 Tf 7.183 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(2)]TJ/F52 5.8022 Tf 3.36 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(/=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(0)]TJ/F191 9.5641 Tf 4.799 0 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(23)]TJ/F52 5.8022 Tf 9.599 -1.435 Td [(k)]TJ/F191 9.5641 Tf 6.172 1.435 Td [(VD)-278(T)]TJ/F51 8.2889 Tf 15.931 0 Td [(1)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(e)]TJ/F51 5.8022 Tf 4.36 3.95 Td [(i)]TJ/F192 6.6948 Tf 1.741 0 Td [(.\031)]TJ/F191 6.6948 Tf 7.183 0 Td [(C)]TJ/F51 5.8022 Tf 5.222 0 Td [(2)]TJ/F52 5.8022 Tf 3.36 0 Td [(k)]TJ/F192 6.6948 Tf 3.017 0 Td [(\031)-100(/=)]TJ/F52 5.8022 Tf 10.33 0 Td [(n)]TJ/F192 9.5641 Tf 3.852 -3.95 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F51 8.2889 Tf 4.76 0 Td [(0)]TJ/F191 9.5641 Tf 4.799 0 Td [(U)]TJ/F192 9.5641 Tf 3.185 0 Td [(;)]TJ/F51 8.2889 Tf -251.433 -16.533 Td [(for)]TJ/F52 8.2889 Tf 12.931 0 Td [(k)]TJ/F191 9.5641 Tf 6.967 0 Td [(D)]TJ/F51 8.2889 Tf 10.116 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.191 0 Td [(n)]TJ/F191 9.5641 Tf 6.917 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(1.)]TJ ET 1 0 0 1 45.354 180.751 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -180.751 cm BT /F51 8.2889 Tf 57.31 170.197 Td [(One)-196(can)-196(then)-196(list)-196(the)-196(edges,)-196(2-cells,)-196(3-cells,)-196(and)-196(4-cells)-196(in)-196(terms)-196(of)-196(the)-196(vertices.)-197(We)-196(now)-196(write)-196(down)]TJ ET 1 0 0 1 45.354 170.197 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -170.197 cm BT /F51 8.2889 Tf 45.354 159.736 Td [(a)-250(few)-250(lists)-250(of)-250(edges)-250(and)-250(2-cells)-250(for)-250(illustration)-250(\050see)]TJ ET 1 0 0 1 237.349 159.736 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -237.349 -159.736 cm BT /F51 8.2889 Tf 237.349 159.736 Td [(Fig.)]TJ ET 1 0 0 1 252.567 159.736 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -252.567 -159.736 cm BT /F51 8.2889 Tf 252.567 159.736 Td [(11)]TJ ET 1 0 0 1 262.165 159.736 cm 0 g 0 G 1 0 0 1 -262.165 -159.736 cm BT /F51 8.2889 Tf 262.165 159.736 Td [(\051.)]TJ ET 1 0 0 1 45.354 159.736 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -159.736 cm BT /F51 8.2889 Tf 57.31 149.181 Td [(Every)-311(edge)-311(lies)-312(on)-311(one)-311(of)-311(the)-312(four)]TJ/F144 8.6077 Tf 132.853 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 3.857 -3.472 Td [('s)-311(defined)-312(by)]TJ/F52 8.2889 Tf 51.572 0 Td [(z)]TJ/F52 5.8022 Tf 3.713 -1.434 Td [(k)]TJ/F191 9.5641 Tf 7.474 1.434 Td [(D)]TJ/F51 8.2889 Tf 11.418 0 Td [(0.)-312(For)-311(example,)-311(the)-311(3)]TJ/F52 8.2889 Tf 81.334 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(2)]TJ/F51 8.2889 Tf 6.437 -3.472 Td [(edges)-311(lying)-311(on)]TJ ET 1 0 0 1 45.354 149.181 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -149.181 cm BT /F52 8.2889 Tf 45.354 138.721 Td [(z)]TJ/F51 5.8022 Tf 3.714 -1.435 Td [(0)]TJ/F191 9.5641 Tf 6.514 1.435 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)-250(are:)]TJ ET 1 0 0 1 45.354 138.721 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -16.51 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -122.211 cm BT /F191 9.5641 Tf 69.265 122.211 Td [(f)]TJ/F52 8.2889 Tf 3.538 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(01)]TJ/F52 5.8022 Tf 9.598 -1.434 Td [(i)]TJ/F192 9.5641 Tf 2.158 1.434 Td [(;)]TJ/F52 8.2889 Tf 6.354 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(02)]TJ/F52 5.8022 Tf 9.599 -1.434 Td [(j)]TJ/F191 9.5641 Tf 2.175 1.434 Td [(g)]TJ/F192 9.5641 Tf 3.538 0 Td [(;)]TJ/F191 9.5641 Tf 13.049 0 Td [(f)]TJ/F52 8.2889 Tf 3.539 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(01)]TJ/F52 5.8022 Tf 9.599 -1.434 Td [(i)]TJ/F192 9.5641 Tf 2.157 1.434 Td [(;)]TJ/F52 8.2889 Tf 6.354 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(03)]TJ/F52 5.8022 Tf 9.598 -1.434 Td [(j)]TJ/F191 9.5641 Tf 2.175 1.434 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(;)]TJ/F191 9.5641 Tf 13.048 0 Td [(f)]TJ/F52 8.2889 Tf 3.539 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(02)]TJ/F52 5.8022 Tf 9.598 -1.434 Td [(i)]TJ/F192 9.5641 Tf 2.158 1.434 Td [(;)]TJ/F52 8.2889 Tf 6.353 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(03)]TJ/F52 5.8022 Tf 9.598 -1.434 Td [(j)]TJ/F191 9.5641 Tf 2.175 1.434 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(;)]TJ ET 1 0 0 1 45.354 122.211 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -122.211 cm BT /F52 8.2889 Tf 45.354 105.796 Td [(i)]TJ/F192 9.5641 Tf 2.371 0 Td [(;)]TJ/F52 8.2889 Tf 4.76 0 Td [(j)]TJ/F191 9.5641 Tf 5.052 0 Td [(D)]TJ/F51 8.2889 Tf 10.116 0 Td [(0)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)-167(:)-166(:)-167(:)-167(;)]TJ/F52 8.2889 Tf 22.191 0 Td [(n)]TJ/F191 9.5641 Tf 6.917 0 Td [(\000)]TJ/F51 8.2889 Tf 9.585 0 Td [(1.)]TJ ET 1 0 0 1 45.354 105.796 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -105.796 cm BT /F51 8.2889 Tf 57.31 95.241 Td [(The)-358(2-cells)-359(are)-358(divided)-358(into)-359(three)-358(groups:)-359(triangles)-358(each)-358(of)-359(which)-358(lies)-358(on)-359(one)-358(of)-359(the)-358(four)]TJ/F144 8.6077 Tf 349.702 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 3.857 -3.472 Td [('s)]TJ ET 1 0 0 1 45.354 95.241 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -95.241 cm BT /F51 8.2889 Tf 45.354 84.78 Td [(defined)-250(by)]TJ/F52 8.2889 Tf 42.34 0 Td [(z)]TJ/F52 5.8022 Tf 3.713 -1.434 Td [(k)]TJ/F191 9.5641 Tf 6.172 1.434 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0;)-250(triangles)-250(each)-250(of)-250(which)-250(has)-250(three)-250(sides)-250(on)-250(three)-250(different)]TJ/F144 8.6077 Tf 228.109 0 Td [(C)]TJ/F108 8.2889 Tf 6.216 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(2)]TJ/F51 8.2889 Tf 3.858 -3.472 Td [('s;)-250(rectangles.)]TJ ET 1 0 0 1 45.354 84.78 cm 0 g 0 G 0 g 0 G 1 0 0 1 -45.354 -84.78 cm BT /F51 8.2889 Tf 57.31 74.226 Td [(For)-250(example,)-250(the)-250(2)]TJ/F52 8.2889 Tf 70.48 0 Td [(n)]TJ/F51 5.8022 Tf 4.79 3.471 Td [(2)]TJ/F51 8.2889 Tf 5.93 -3.471 Td [(triangles)-250(lying)-250(on)]TJ/F52 8.2889 Tf 68.284 0 Td [(z)]TJ/F51 5.8022 Tf 3.713 -1.435 Td [(0)]TJ/F191 9.5641 Tf 6.514 1.435 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)-250(are:)]TJ ET 1 0 0 1 45.354 74.226 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -16.51 cm 0 g 0 G 0 g 0 G 1 0 0 1 -41.369 -57.716 cm BT /F191 9.5641 Tf 69.265 57.716 Td [(f)]TJ/F52 8.2889 Tf 3.538 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(01)]TJ/F52 5.8022 Tf 9.598 -1.434 Td [(i)]TJ/F192 9.5641 Tf 2.158 1.434 Td [(;)]TJ/F52 8.2889 Tf 6.354 0 Td [(p)]TJ/F51 8.2889 Tf 4.608 0 Td [(02)]TJ/F52 5.8022 Tf 9.599 -1.434 Td [(j)]TJ/F192 9.5641 Tf 2.175 1.434 Td [(;)]TJ/F52 8.2889 Tf 6.353 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(03)]TJ/F52 5.8022 Tf 9.598 -1.434 Td [(k)]TJ/F191 9.5641 Tf 3.516 1.434 Td [(g)]TJ/F192 9.5641 Tf 3.538 0 Td [(;)]TJ/F52 8.2889 Tf 13.049 0 Td [(i)]TJ/F191 9.5641 Tf 4.496 0 Td [(\000)]TJ/F52 8.2889 Tf 9.585 0 Td [(j)]TJ/F191 9.5641 Tf 4.521 0 Td [(C)]TJ/F52 8.2889 Tf 9.585 0 Td [(k)]TJ/F191 9.5641 Tf 6.967 0 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)-192(or)]TJ/F191 9.5641 Tf 16.085 0 Td [(\000)]TJ/F51 8.2889 Tf 7.46 0 Td [(1)]TJ/F192 9.5641 Tf 13.088 0 Td [(.)]TJ/F51 8.2889 Tf 3.568 0 Td [(mod)]TJ/F52 8.2889 Tf 19.387 0 Td 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[(0)]TJ/F191 9.5641 Tf 6.515 1.435 Td [(D)]TJ/F51 8.2889 Tf 10.116 0 Td [(0)-222(and)-222(an)-222(opposite)-222(edge)-222(on)]TJ/F52 8.2889 Tf 100.217 0 Td [(z)]TJ/F52 5.8022 Tf 3.714 -1.435 Td [(m)]TJ/F191 9.5641 Tf 8.167 1.435 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)]TJ/F192 9.5641 Tf 4.799 0 Td [(;)]TJ/F52 8.2889 Tf 6.6 0 Td [(m)]TJ/F191 9.5641 Tf 9.818 0 Td [(D)]TJ/F51 8.2889 Tf 10.116 0 Td [(1)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(2)]TJ/F192 9.5641 Tf 4.8 0 Td [(;)]TJ/F51 8.2889 Tf 4.759 0 Td [(3.)-222(The)-222(group)-222(with)]TJ/F52 8.2889 Tf 68.366 0 Td [(m)]TJ/F191 9.5641 Tf 9.818 0 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(1,)-222(for)-222(example,)-222(contains)]TJ ET 1 0 0 1 39.797 397.593 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -397.593 cm BT /F51 8.2889 Tf 39.797 387.132 Td [(the)-250(following)]TJ/F52 8.2889 Tf 52.858 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(3)]TJ/F51 8.2889 Tf 5.93 -3.472 Td [(rectangles:)]TJ ET 1 0 0 1 39.797 387.132 cm 0 g 0 G 0 g 0 G 1 0 0 1 -3.985 -14.034 cm 0 g 0 G 0 g 0 G 1 0 0 1 -35.812 -373.098 cm BT /F191 9.5641 Tf 63.707 373.098 Td [(f)]TJ/F52 8.2889 Tf 3.539 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(02)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(i)]TJ/F192 9.5641 Tf 2.158 1.435 Td [(;)]TJ/F52 8.2889 Tf 6.353 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(03)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(j)]TJ/F192 9.5641 Tf 2.175 1.435 Td [(;)]TJ/F52 8.2889 Tf 6.354 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(13)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(k)]TJ/F192 9.5641 Tf 3.515 1.435 Td [(;)]TJ/F52 8.2889 Tf 6.354 0 Td [(p)]TJ/F51 8.2889 Tf 4.609 0 Td [(12)]TJ/F52 5.8022 Tf 9.598 -1.435 Td [(l)]TJ/F191 9.5641 Tf 2.088 1.435 Td [(g)]TJ/F192 9.5641 Tf 3.539 0 Td [(;)]TJ/F52 8.2889 Tf 13.048 0 Td [(i)]TJ/F191 9.5641 Tf 4.496 0 Td [(\000)]TJ/F52 8.2889 Tf 9.585 0 Td [(j)]TJ/F191 9.5641 Tf 4.521 0 Td [(C)]TJ/F52 8.2889 Tf 9.586 0 Td [(k)]TJ/F191 9.5641 Tf 6.435 0 Td [(\000)]TJ/F52 8.2889 Tf 9.585 0 Td [(l)]TJ/F191 9.5641 Tf 4.928 0 Td [(D)]TJ/F51 8.2889 Tf 10.117 0 Td [(0)]TJ/F192 9.5641 Tf 6.871 0 Td [(.)]TJ/F51 8.2889 Tf 3.568 0 Td [(mod)]TJ/F52 8.2889 Tf 19.387 0 Td [(n)]TJ/F192 9.5641 Tf 4.791 0 Td [(/:)]TJ ET 1 0 0 1 39.797 373.098 cm 0 g 0 G 0 g 0 G 1 0 0 1 11.955 -15.299 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -51.752 -357.799 cm BT /F51 8.2889 Tf 51.752 357.799 Td [(Fig.)]TJ ET 1 0 0 1 66.979 357.799 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -66.979 -357.799 cm BT /F51 8.2889 Tf 66.979 357.799 Td [(12)]TJ ET 1 0 0 1 76.577 357.799 cm 0 g 0 G 1 0 0 1 -76.577 -357.799 cm BT /F51 8.2889 Tf 78.657 357.799 Td [(is)-251(an)-251(actual)-251(image)-251(of)-251(a)-251(generic)-251(4-cell)-251(using)-251(an)-251(explicit)-251(embedding)-251(of)]TJ/F144 8.6077 Tf 259.266 0 Td [(C)]TJ/F108 8.2889 Tf 6.217 0 Td [(P)]TJ/F51 5.8022 Tf 5.197 3.472 Td [(3)]TJ/F51 8.2889 Tf 5.938 -3.472 Td [(into)]TJ/F144 8.6077 Tf 17.382 0 Td [(R)]TJ/F51 5.8022 Tf 6.216 3.472 Td [(16)]TJ/F51 8.2889 Tf 9.298 -3.472 Td [(\050see,)-251(e.g.,)]TJ ET 1 0 0 1 39.797 357.799 cm 0 g 0 G 0 g 0 G 1 0 0 1 0 -10.461 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -39.797 -347.338 cm BT /F51 8.2889 Tf 39.797 347.338 Td [(Hanson)-198(and)-199(Sha)]TJ ET 1 0 0 1 99.931 347.338 cm 0 g 0 G 1 0 0 1 -99.931 -347.338 cm BT /F51 8.2889 Tf 101.576 347.338 Td [(\050)]TJ ET 1 0 0 1 104.643 347.338 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -104.643 -347.338 cm BT /F51 8.2889 Tf 104.643 347.338 Td [(2006)]TJ ET 1 0 0 1 123.84 347.338 cm 0 g 0 G 1 0 0 1 -123.84 -347.338 cm BT /F51 8.2889 Tf 123.84 347.338 Td [(\051\051.)-199(\050a\051)-198(and)-199(\050b\051)-198(depict)-198(the)-199(3-balls)-198(that)-199(are)-198(the)-199(upper)-198(and)-198(lower)-199(hemispheres)-198(of)-199(the)]TJ ET 1 0 0 1 39.797 347.338 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -347.338 cm BT /F52 8.2889 Tf 39.797 336.877 Td [(S)]TJ/F51 5.8022 Tf 4.621 3.472 Td [(3)]TJ/F51 8.2889 Tf 5.566 -3.472 Td [(bounding)-206(the)-206(4-cell)-206(\050see)-206(also)]TJ ET 1 0 0 1 159.584 336.877 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -159.584 -336.877 cm BT /F51 8.2889 Tf 159.584 336.877 Td [(Fig.)]TJ ET 1 0 0 1 174.438 336.877 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -174.438 -336.877 cm BT /F51 8.2889 Tf 174.438 336.877 Td [(6)]TJ ET 1 0 0 1 179.237 336.877 cm 0 g 0 G 1 0 0 1 -179.237 -336.877 cm BT /F51 8.2889 Tf 179.237 336.877 Td [(\051.)-206(Note)-207(the)-206(distinct)-206(rectangles,)-206(which)-206(cut)-206(across)-206(the)-206(middle)-206(of)-206(the)]TJ ET 1 0 0 1 39.797 336.877 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -336.877 cm BT /F51 8.2889 Tf 39.797 326.417 Td [(two)-245(3-balls,)-244(dividing)-245(each)-245(into)-244(two)-245(pyramids;)-245(one)-244(pyramid)-245(in)-245(each)-244(3-ball)-245(has)-245(been)-244(made)-245(transparent)]TJ ET 1 0 0 1 39.797 326.417 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -326.417 cm BT /F51 8.2889 Tf 39.797 315.956 Td [(using)-249(wire-frame)-249(rendering)-249(to)-249(make)-249(the)-249(rectangle)-250(visible.)-249(\050c\051)-249(shows)-249(a)-249(complete)-249(partially)-249(transparent)]TJ ET 1 0 0 1 39.797 315.956 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -315.956 cm BT /F51 8.2889 Tf 39.797 305.495 Td [(shaded)-355(rendering)-355(of)-355(the)-355(entire)-355(embedded)-355(4-cell)-355(projec)1(ted)-355(to)-355(3D,)-355(with)-355(the)-355(outer)-355(octahedron)-355(being)]TJ ET 1 0 0 1 39.797 305.495 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -305.495 cm BT /F51 8.2889 Tf 39.797 295.034 Td [(essentially)-250(the)-250(equator)]TJ/F52 8.2889 Tf 88.881 0 Td [(S)]TJ/F51 5.8022 Tf 4.621 3.472 Td [(2)]TJ/F51 8.2889 Tf 5.93 -3.472 Td [(that)-250(is)-250(shared)-250(by)-250(the)-250(two)-250(hemispheres)-250(\050a\051)-250(and)-250(\050b\051)-250(of)-250(the)]TJ/F52 8.2889 Tf 213.554 0 Td [(S)]TJ/F51 5.8022 Tf 4.621 3.472 Td [(3)]TJ/F51 8.2889 Tf 3.857 -3.472 Td [(.)]TJ ET 1 0 0 1 39.797 295.034 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -295.034 cm BT /F51 8.2889 Tf 51.752 284.717 Td [(Finally,)-235(we)-236(briefly)-235(indicate)-236(how)-235(tessellation)-236(can)-235(help)-236(in)-235(computer)-235(graphics)-236(visualization)-235(of)-236(Fermat)]TJ ET 1 0 0 1 39.797 284.717 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -284.717 cm BT /F51 8.2889 Tf 39.797 274.256 Td [(surfaces.)-232(We)-233(first)-232(embed)-233(the)-232(edges)-232(of)-233(a)-232(single)-232(3-cell)-233(in)]TJ/F144 8.6077 Tf 206.47 0 Td [(R)]TJ/F51 5.8022 Tf 6.216 3.472 Td [(16)]TJ/F51 8.2889 Tf 9.143 -3.472 Td [(using)-232(our)-233(standard)-232(embedding)-233(of)]TJ/F144 8.6077 Tf 127.582 0 Td [(C)]TJ/F108 8.2889 Tf 6.216 0 Td [(P)]TJ/F51 5.8022 Tf 5.198 3.472 Td [(3)]TJ/F51 8.2889 Tf 3.857 -3.472 Td [(.)-233(Th)1(e)]TJ ET 1 0 0 1 39.797 274.256 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -274.256 cm BT /F51 8.2889 Tf 39.797 263.795 Td [(group)]TJ/F192 9.2055 Tf 24.648 0 Td [(\000)]TJ/F52 5.8022 Tf 5.726 -1.434 Td [(n)]TJ/F51 8.2889 Tf 5.971 1.434 Td [(\050which)-256(has)-255(order)-256(24)]TJ/F52 8.2889 Tf 76.449 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(3)]TJ/F51 8.2889 Tf 3.857 -3.472 Td [(\051)-256(acts)-255(transitively)-256(on)-256(the)-255(set)-256(of)-256(all)-255(the)-256(3-cells)-256(with)-255(the)-256(isotropy)-256(group)]TJ ET 1 0 0 1 39.797 263.795 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -263.795 cm BT /F144 8.6077 Tf 39.797 253.335 Td [(Z)]TJ/F51 5.8022 Tf 5.738 -1.435 Td [(2)]TJ/F51 8.2889 Tf 6.601 1.435 Td [(for)-331(the)-331(single)-331(3-cell.)-331(Using)-331(computer)-331(algebra)-331(tools)-331(we)-331(produce)-331(a)-331(representative)-331(from)-330(each)-331(two-)]TJ ET 1 0 0 1 39.797 253.335 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -253.335 cm BT /F51 8.2889 Tf 39.797 242.874 Td [(element)-212(equivalence)-213(class)-212(of)]TJ/F192 9.2055 Tf 109.659 0 Td [(\000)]TJ/F52 5.8022 Tf 5.726 -1.435 Td [(n)]TJ/F192 9.5641 Tf 3.852 1.435 Td [(=)]TJ/F144 8.6077 Tf 4.495 0 Td [(Z)]TJ/F51 5.8022 Tf 5.739 -1.435 Td [(2)]TJ/F51 8.2889 Tf 3.857 1.435 Td [(,)-212(and)-213(then)-212(we)-213(can)-212(generate)-213(all)-212(distinct)-213(12)]TJ/F52 8.2889 Tf 153.548 0 Td [(n)]TJ/F51 5.8022 Tf 4.791 3.472 Td [(3)]TJ/F51 8.2889 Tf 5.618 -3.472 Td [(3-cells.)-213(One)-212(also)-213(needs)]TJ ET 1 0 0 1 39.797 242.874 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -242.874 cm BT /F51 8.2889 Tf 39.797 232.413 Td [(to)-186(choose)-185(appropriate)-186(projections)-186(to)-185(3D)-186(to)-185(create)-186(the)-186(picture.)-186(This)-185(process)-186(becomes)-186(very)-185(complex)-186(even)]TJ ET 1 0 0 1 39.797 232.413 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -232.413 cm BT /F51 8.2889 Tf 39.797 221.952 Td [(for)]TJ/F52 8.2889 Tf 13.091 0 Td [(F)]TJ/F51 5.8022 Tf 4.028 -1.434 Td [(4)]TJ/F51 8.2889 Tf 6.091 1.434 Td [(\050a)-269(K3)-270(surface\051,)-269(which)-269(has)-270(768)-269(3-cells.)-270(W)1(ith)-270(appropriate)-269(3D)-270(projecti)1(ons,)-270(we)-269(can)-270(display)-269(various)]TJ ET 1 0 0 1 39.797 221.952 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -221.952 cm BT /F51 8.2889 Tf 39.797 211.491 Td [(parts)-262(of)]TJ/F52 8.2889 Tf 31.247 0 Td [(F)]TJ/F51 5.8022 Tf 4.028 -1.434 Td [(4)]TJ/F51 8.2889 Tf 3.858 1.434 Td [(,)-262(and)-263(hence)-262(have)-262(a)-263(glance)-262(at)-263(its)-262(structure.)]TJ ET 1 0 0 1 238.088 211.491 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -238.088 -211.491 cm BT /F51 8.2889 Tf 238.088 211.491 Td [(Fig.)]TJ ET 1 0 0 1 253.409 211.491 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -253.409 -211.491 cm BT /F51 8.2889 Tf 253.409 211.491 Td [(13)]TJ ET 1 0 0 1 263.007 211.491 cm 0 g 0 G 1 0 0 1 -263.007 -211.491 cm BT /F51 8.2889 Tf 265.182 211.491 Td [(shows)-262(the)-263(chosen)-262(basic)-262(representative)-263(3-)]TJ ET 1 0 0 1 39.797 211.491 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -211.491 cm BT /F51 8.2889 Tf 39.797 201.031 Td [(cell;)]TJ ET 1 0 0 1 58.161 201.031 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -58.161 -201.031 cm BT /F51 8.2889 Tf 58.161 201.031 Td [(Fig.)]TJ ET 1 0 0 1 73.466 201.031 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -73.466 -201.031 cm BT /F51 8.2889 Tf 73.466 201.031 Td [(14)]TJ ET 1 0 0 1 83.064 201.031 cm 0 g 0 G 1 0 0 1 -83.064 -201.031 cm BT /F51 8.2889 Tf 85.223 201.031 Td [(presents)-260(four)-261(3-cells)-260(generated)-261(from)-260(the)-261(representatives)-260(of)]TJ/F192 9.2055 Tf 226.739 0 Td [(\000)]TJ/F51 5.8022 Tf 5.726 -1.435 Td [(4)]TJ/F192 9.5641 Tf 3.858 1.435 Td [(=)]TJ/F144 8.6077 Tf 4.495 0 Td [(Z)]TJ/F51 5.8022 Tf 5.738 -1.435 Td [(2)]TJ/F51 8.2889 Tf 6.017 1.435 Td [(that)-260(form)-261(the)-260(isotropy)]TJ ET 1 0 0 1 39.797 201.031 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -201.031 cm BT /F51 8.2889 Tf 39.797 190.57 Td [(group,)-210(in)]TJ/F192 9.2055 Tf 35.454 0 Td [(\000)]TJ/F51 5.8022 Tf 5.725 -1.435 Td [(4)]TJ/F51 8.2889 Tf 3.858 1.435 Td [(,)-210(of)-209(the)-210(quadrilateral)-209(base)-210(of)-210(the)-209(basic)-210(3-cell.)]TJ ET 1 0 0 1 251.463 190.57 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -251.463 -190.57 cm BT /F51 8.2889 Tf 251.463 190.57 Td [(Fig.)]TJ ET 1 0 0 1 266.347 190.57 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -266.347 -190.57 cm BT /F51 8.2889 Tf 266.347 190.57 Td [(15)]TJ ET 1 0 0 1 275.945 190.57 cm 0 g 0 G 1 0 0 1 -275.945 -190.57 cm BT /F51 8.2889 Tf 277.683 190.57 Td [(shows)-210(the)-209(three)-210(sets)-209(of)-210(four)-210(rectangles)]TJ ET 1 0 0 1 39.797 190.57 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -190.57 cm BT /F51 8.2889 Tf 39.797 180.109 Td [(sharing)-169(one)-170(edge)-169(of)-169(a)-170(fixed)-169(triangle;)-169(each)-170(vertex)-169(not)-169(on)-170(the)-169(triangle)-169(is)-170(shared)-169(by)-169(two)-169(of)-170(these)-169(rectangles,)]TJ ET 1 0 0 1 39.797 180.109 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -180.109 cm BT /F51 8.2889 Tf 39.797 169.648 Td [(so)-226(15)-227(of)-226(the)-227(24)-226(vertices)-226(are)-227(generated)-226(in)-227(this)-226(way.)]TJ ET 1 0 0 1 227.901 169.648 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -227.901 -169.648 cm BT /F51 8.2889 Tf 227.901 169.648 Td [(Fig.)]TJ ET 1 0 0 1 242.923 169.648 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -242.923 -169.648 cm BT /F51 8.2889 Tf 242.923 169.648 Td [(16)]TJ ET 1 0 0 1 252.522 169.648 cm 0 g 0 G 1 0 0 1 -252.522 -169.648 cm BT /F51 8.2889 Tf 254.398 169.648 Td [(uses)-226(a)-227(projection)-226(that)-227(exposes)-226(all)-226(24)-227(vertices)]TJ ET 1 0 0 1 39.797 169.648 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -169.648 cm BT /F51 8.2889 Tf 39.797 159.188 Td [(and)-260(draws)-260(schematic)-260(straight)-260(lines)-260(between)-260(them,)-260(with)-260(the)-260(shape)-260(of)-260(the)-260(basic)-260(3-cell)-260(shown)-260(in)-260(heavy)]TJ ET 1 0 0 1 39.797 159.188 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -159.188 cm BT /F51 8.2889 Tf 39.797 148.727 Td [(lines.)-325(Finally,)]TJ ET 1 0 0 1 92.638 148.727 cm 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -92.638 -148.727 cm BT /F51 8.2889 Tf 92.638 148.727 Td [(Fig.)]TJ ET 1 0 0 1 108.476 148.727 cm 0 g 0 G 0 0 .4 rg 0 0 .4 RG 1 0 0 1 -108.476 -148.727 cm BT /F51 8.2889 Tf 108.476 148.727 Td [(17)]TJ ET 1 0 0 1 118.074 148.727 cm 0 g 0 G 1 0 0 1 -118.074 -148.727 cm BT /F51 8.2889 Tf 120.766 148.727 Td [(presents)-325(a)-324(similar)-325(projection)-325(of)-325(the)-324(correctly)-325(rendered)-325(edges)-324(for)-325(the)-325(entire)-325(K3)]TJ ET 1 0 0 1 39.797 148.727 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -148.727 cm BT /F51 8.2889 Tf 39.797 138.266 Td [(surface,)-250(giving)-250(a)-250(qualitative)-250(representation)-250(of)-250(a)-250(full)-250(tessellation)-250(based)-250(on)-250(our)-250(construction.)]TJ ET 1 0 0 1 39.797 138.266 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -138.266 cm BT /F51 8.2889 Tf 51.752 127.949 Td [(Further)-173(exploration)-174(of)-173(the)-173(properties)-173(of)-174(the)-173(family)-173(of)-173(tessellations)-174(we)-173(have)-173(presented)-173(requires)-174(more)]TJ ET 1 0 0 1 39.797 127.949 cm 0 g 0 G 0 g 0 G 1 0 0 1 -39.797 -127.949 cm BT /F51 8.2889 Tf 39.797 117.488 Td 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F"]vuvvVVV|qTj2R TUU]tfK$ӧOۊKN}z]zzX,NNNv:G,oݺð/_`t:I%r#ӛ7o"B;vL"8pkڵNJxk7FO7z¸ƍ0nq'=a FO7z¸ƍ0nq'=a FO7z¸ƍ0nq'=a FO7z¸ƍ*=endstream endobj 285 0 obj <>stream pdfTeX-1.40.3 application/pdf A tessellation for Fermat surfaces in CP3 A.J. Hanson; J.-P. Sha TessellationFermat surfaceK3 surfaceComplex projective space journal Journal of Symbolic Computation Copyright © 2008 Elsevier Ltd. All rights reserved. Elsevier Ltd 0747-7171 44 6 June 2009 Journal of Symbolic Computation 591-605 591 605 10.1016/j.jsc.2008.09.002 http://dx.doi.org/10.1016/j.jsc.2008.09.002 doi:10.1016/j.jsc.2008.09.002 sciencedirect.com elsevier.com 1 B Elsevier True 2009-03-24T09:23:31+05:30 2009-03-24T09:23:31+05:30 2009-03-24T09:23:31+05:30 endstream endobj 286 0 obj <>stream xڝwTTϽwz0z.0. 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