Polytope of Type {738}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {738}*1476
Also Known As : 738-gon, {738}. if this polytope has another name.
Group : SmallGroup(1476,11)
Rank : 2
Schlafli Type : {738}
Number of vertices, edges, etc : 738, 738
Order of s₀s₁ : 738
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {369}*738
   3-fold quotients : {246}*492
   6-fold quotients : {123}*246
   9-fold quotients : {82}*164
   18-fold quotients : {41}*82
   41-fold quotients : {18}*36
   82-fold quotients : {9}*18
   123-fold quotients : {6}*12
   246-fold quotients : {3}*6
   369-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2,  3)(  4,121)(  5,123)(  6,122)(  7,118)(  8,120)(  9,119)( 10,115)
( 11,117)( 12,116)( 13,112)( 14,114)( 15,113)( 16,109)( 17,111)( 18,110)
( 19,106)( 20,108)( 21,107)( 22,103)( 23,105)( 24,104)( 25,100)( 26,102)
( 27,101)( 28, 97)( 29, 99)( 30, 98)( 31, 94)( 32, 96)( 33, 95)( 34, 91)
( 35, 93)( 36, 92)( 37, 88)( 38, 90)( 39, 89)( 40, 85)( 41, 87)( 42, 86)
( 43, 82)( 44, 84)( 45, 83)( 46, 79)( 47, 81)( 48, 80)( 49, 76)( 50, 78)
( 51, 77)( 52, 73)( 53, 75)( 54, 74)( 55, 70)( 56, 72)( 57, 71)( 58, 67)
( 59, 69)( 60, 68)( 61, 64)( 62, 66)( 63, 65)(124,248)(125,247)(126,249)
(127,368)(128,367)(129,369)(130,365)(131,364)(132,366)(133,362)(134,361)
(135,363)(136,359)(137,358)(138,360)(139,356)(140,355)(141,357)(142,353)
(143,352)(144,354)(145,350)(146,349)(147,351)(148,347)(149,346)(150,348)
(151,344)(152,343)(153,345)(154,341)(155,340)(156,342)(157,338)(158,337)
(159,339)(160,335)(161,334)(162,336)(163,332)(164,331)(165,333)(166,329)
(167,328)(168,330)(169,326)(170,325)(171,327)(172,323)(173,322)(174,324)
(175,320)(176,319)(177,321)(178,317)(179,316)(180,318)(181,314)(182,313)
(183,315)(184,311)(185,310)(186,312)(187,308)(188,307)(189,309)(190,305)
(191,304)(192,306)(193,302)(194,301)(195,303)(196,299)(197,298)(198,300)
(199,296)(200,295)(201,297)(202,293)(203,292)(204,294)(205,290)(206,289)
(207,291)(208,287)(209,286)(210,288)(211,284)(212,283)(213,285)(214,281)
(215,280)(216,282)(217,278)(218,277)(219,279)(220,275)(221,274)(222,276)
(223,272)(224,271)(225,273)(226,269)(227,268)(228,270)(229,266)(230,265)
(231,267)(232,263)(233,262)(234,264)(235,260)(236,259)(237,261)(238,257)
(239,256)(240,258)(241,254)(242,253)(243,255)(244,251)(245,250)(246,252)
(371,372)(373,490)(374,492)(375,491)(376,487)(377,489)(378,488)(379,484)
(380,486)(381,485)(382,481)(383,483)(384,482)(385,478)(386,480)(387,479)
(388,475)(389,477)(390,476)(391,472)(392,474)(393,473)(394,469)(395,471)
(396,470)(397,466)(398,468)(399,467)(400,463)(401,465)(402,464)(403,460)
(404,462)(405,461)(406,457)(407,459)(408,458)(409,454)(410,456)(411,455)
(412,451)(413,453)(414,452)(415,448)(416,450)(417,449)(418,445)(419,447)
(420,446)(421,442)(422,444)(423,443)(424,439)(425,441)(426,440)(427,436)
(428,438)(429,437)(430,433)(431,435)(432,434)(493,617)(494,616)(495,618)
(496,737)(497,736)(498,738)(499,734)(500,733)(501,735)(502,731)(503,730)
(504,732)(505,728)(506,727)(507,729)(508,725)(509,724)(510,726)(511,722)
(512,721)(513,723)(514,719)(515,718)(516,720)(517,716)(518,715)(519,717)
(520,713)(521,712)(522,714)(523,710)(524,709)(525,711)(526,707)(527,706)
(528,708)(529,704)(530,703)(531,705)(532,701)(533,700)(534,702)(535,698)
(536,697)(537,699)(538,695)(539,694)(540,696)(541,692)(542,691)(543,693)
(544,689)(545,688)(546,690)(547,686)(548,685)(549,687)(550,683)(551,682)
(552,684)(553,680)(554,679)(555,681)(556,677)(557,676)(558,678)(559,674)
(560,673)(561,675)(562,671)(563,670)(564,672)(565,668)(566,667)(567,669)
(568,665)(569,664)(570,666)(571,662)(572,661)(573,663)(574,659)(575,658)
(576,660)(577,656)(578,655)(579,657)(580,653)(581,652)(582,654)(583,650)
(584,649)(585,651)(586,647)(587,646)(588,648)(589,644)(590,643)(591,645)
(592,641)(593,640)(594,642)(595,638)(596,637)(597,639)(598,635)(599,634)
(600,636)(601,632)(602,631)(603,633)(604,629)(605,628)(606,630)(607,626)
(608,625)(609,627)(610,623)(611,622)(612,624)(613,620)(614,619)(615,621);;
s1 := (  1,496)(  2,498)(  3,497)(  4,493)(  5,495)(  6,494)(  7,613)(  8,615)
(  9,614)( 10,610)( 11,612)( 12,611)( 13,607)( 14,609)( 15,608)( 16,604)
( 17,606)( 18,605)( 19,601)( 20,603)( 21,602)( 22,598)( 23,600)( 24,599)
( 25,595)( 26,597)( 27,596)( 28,592)( 29,594)( 30,593)( 31,589)( 32,591)
( 33,590)( 34,586)( 35,588)( 36,587)( 37,583)( 38,585)( 39,584)( 40,580)
( 41,582)( 42,581)( 43,577)( 44,579)( 45,578)( 46,574)( 47,576)( 48,575)
( 49,571)( 50,573)( 51,572)( 52,568)( 53,570)( 54,569)( 55,565)( 56,567)
( 57,566)( 58,562)( 59,564)( 60,563)( 61,559)( 62,561)( 63,560)( 64,556)
( 65,558)( 66,557)( 67,553)( 68,555)( 69,554)( 70,550)( 71,552)( 72,551)
( 73,547)( 74,549)( 75,548)( 76,544)( 77,546)( 78,545)( 79,541)( 80,543)
( 81,542)( 82,538)( 83,540)( 84,539)( 85,535)( 86,537)( 87,536)( 88,532)
( 89,534)( 90,533)( 91,529)( 92,531)( 93,530)( 94,526)( 95,528)( 96,527)
( 97,523)( 98,525)( 99,524)(100,520)(101,522)(102,521)(103,517)(104,519)
(105,518)(106,514)(107,516)(108,515)(109,511)(110,513)(111,512)(112,508)
(113,510)(114,509)(115,505)(116,507)(117,506)(118,502)(119,504)(120,503)
(121,499)(122,501)(123,500)(124,373)(125,375)(126,374)(127,370)(128,372)
(129,371)(130,490)(131,492)(132,491)(133,487)(134,489)(135,488)(136,484)
(137,486)(138,485)(139,481)(140,483)(141,482)(142,478)(143,480)(144,479)
(145,475)(146,477)(147,476)(148,472)(149,474)(150,473)(151,469)(152,471)
(153,470)(154,466)(155,468)(156,467)(157,463)(158,465)(159,464)(160,460)
(161,462)(162,461)(163,457)(164,459)(165,458)(166,454)(167,456)(168,455)
(169,451)(170,453)(171,452)(172,448)(173,450)(174,449)(175,445)(176,447)
(177,446)(178,442)(179,444)(180,443)(181,439)(182,441)(183,440)(184,436)
(185,438)(186,437)(187,433)(188,435)(189,434)(190,430)(191,432)(192,431)
(193,427)(194,429)(195,428)(196,424)(197,426)(198,425)(199,421)(200,423)
(201,422)(202,418)(203,420)(204,419)(205,415)(206,417)(207,416)(208,412)
(209,414)(210,413)(211,409)(212,411)(213,410)(214,406)(215,408)(216,407)
(217,403)(218,405)(219,404)(220,400)(221,402)(222,401)(223,397)(224,399)
(225,398)(226,394)(227,396)(228,395)(229,391)(230,393)(231,392)(232,388)
(233,390)(234,389)(235,385)(236,387)(237,386)(238,382)(239,384)(240,383)
(241,379)(242,381)(243,380)(244,376)(245,378)(246,377)(247,620)(248,619)
(249,621)(250,617)(251,616)(252,618)(253,737)(254,736)(255,738)(256,734)
(257,733)(258,735)(259,731)(260,730)(261,732)(262,728)(263,727)(264,729)
(265,725)(266,724)(267,726)(268,722)(269,721)(270,723)(271,719)(272,718)
(273,720)(274,716)(275,715)(276,717)(277,713)(278,712)(279,714)(280,710)
(281,709)(282,711)(283,707)(284,706)(285,708)(286,704)(287,703)(288,705)
(289,701)(290,700)(291,702)(292,698)(293,697)(294,699)(295,695)(296,694)
(297,696)(298,692)(299,691)(300,693)(301,689)(302,688)(303,690)(304,686)
(305,685)(306,687)(307,683)(308,682)(309,684)(310,680)(311,679)(312,681)
(313,677)(314,676)(315,678)(316,674)(317,673)(318,675)(319,671)(320,670)
(321,672)(322,668)(323,667)(324,669)(325,665)(326,664)(327,666)(328,662)
(329,661)(330,663)(331,659)(332,658)(333,660)(334,656)(335,655)(336,657)
(337,653)(338,652)(339,654)(340,650)(341,649)(342,651)(343,647)(344,646)
(345,648)(346,644)(347,643)(348,645)(349,641)(350,640)(351,642)(352,638)
(353,637)(354,639)(355,635)(356,634)(357,636)(358,632)(359,631)(360,633)
(361,629)(362,628)(363,630)(364,626)(365,625)(366,627)(367,623)(368,622)
(369,624);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(738)!(  2,  3)(  4,121)(  5,123)(  6,122)(  7,118)(  8,120)(  9,119)
( 10,115)( 11,117)( 12,116)( 13,112)( 14,114)( 15,113)( 16,109)( 17,111)
( 18,110)( 19,106)( 20,108)( 21,107)( 22,103)( 23,105)( 24,104)( 25,100)
( 26,102)( 27,101)( 28, 97)( 29, 99)( 30, 98)( 31, 94)( 32, 96)( 33, 95)
( 34, 91)( 35, 93)( 36, 92)( 37, 88)( 38, 90)( 39, 89)( 40, 85)( 41, 87)
( 42, 86)( 43, 82)( 44, 84)( 45, 83)( 46, 79)( 47, 81)( 48, 80)( 49, 76)
( 50, 78)( 51, 77)( 52, 73)( 53, 75)( 54, 74)( 55, 70)( 56, 72)( 57, 71)
( 58, 67)( 59, 69)( 60, 68)( 61, 64)( 62, 66)( 63, 65)(124,248)(125,247)
(126,249)(127,368)(128,367)(129,369)(130,365)(131,364)(132,366)(133,362)
(134,361)(135,363)(136,359)(137,358)(138,360)(139,356)(140,355)(141,357)
(142,353)(143,352)(144,354)(145,350)(146,349)(147,351)(148,347)(149,346)
(150,348)(151,344)(152,343)(153,345)(154,341)(155,340)(156,342)(157,338)
(158,337)(159,339)(160,335)(161,334)(162,336)(163,332)(164,331)(165,333)
(166,329)(167,328)(168,330)(169,326)(170,325)(171,327)(172,323)(173,322)
(174,324)(175,320)(176,319)(177,321)(178,317)(179,316)(180,318)(181,314)
(182,313)(183,315)(184,311)(185,310)(186,312)(187,308)(188,307)(189,309)
(190,305)(191,304)(192,306)(193,302)(194,301)(195,303)(196,299)(197,298)
(198,300)(199,296)(200,295)(201,297)(202,293)(203,292)(204,294)(205,290)
(206,289)(207,291)(208,287)(209,286)(210,288)(211,284)(212,283)(213,285)
(214,281)(215,280)(216,282)(217,278)(218,277)(219,279)(220,275)(221,274)
(222,276)(223,272)(224,271)(225,273)(226,269)(227,268)(228,270)(229,266)
(230,265)(231,267)(232,263)(233,262)(234,264)(235,260)(236,259)(237,261)
(238,257)(239,256)(240,258)(241,254)(242,253)(243,255)(244,251)(245,250)
(246,252)(371,372)(373,490)(374,492)(375,491)(376,487)(377,489)(378,488)
(379,484)(380,486)(381,485)(382,481)(383,483)(384,482)(385,478)(386,480)
(387,479)(388,475)(389,477)(390,476)(391,472)(392,474)(393,473)(394,469)
(395,471)(396,470)(397,466)(398,468)(399,467)(400,463)(401,465)(402,464)
(403,460)(404,462)(405,461)(406,457)(407,459)(408,458)(409,454)(410,456)
(411,455)(412,451)(413,453)(414,452)(415,448)(416,450)(417,449)(418,445)
(419,447)(420,446)(421,442)(422,444)(423,443)(424,439)(425,441)(426,440)
(427,436)(428,438)(429,437)(430,433)(431,435)(432,434)(493,617)(494,616)
(495,618)(496,737)(497,736)(498,738)(499,734)(500,733)(501,735)(502,731)
(503,730)(504,732)(505,728)(506,727)(507,729)(508,725)(509,724)(510,726)
(511,722)(512,721)(513,723)(514,719)(515,718)(516,720)(517,716)(518,715)
(519,717)(520,713)(521,712)(522,714)(523,710)(524,709)(525,711)(526,707)
(527,706)(528,708)(529,704)(530,703)(531,705)(532,701)(533,700)(534,702)
(535,698)(536,697)(537,699)(538,695)(539,694)(540,696)(541,692)(542,691)
(543,693)(544,689)(545,688)(546,690)(547,686)(548,685)(549,687)(550,683)
(551,682)(552,684)(553,680)(554,679)(555,681)(556,677)(557,676)(558,678)
(559,674)(560,673)(561,675)(562,671)(563,670)(564,672)(565,668)(566,667)
(567,669)(568,665)(569,664)(570,666)(571,662)(572,661)(573,663)(574,659)
(575,658)(576,660)(577,656)(578,655)(579,657)(580,653)(581,652)(582,654)
(583,650)(584,649)(585,651)(586,647)(587,646)(588,648)(589,644)(590,643)
(591,645)(592,641)(593,640)(594,642)(595,638)(596,637)(597,639)(598,635)
(599,634)(600,636)(601,632)(602,631)(603,633)(604,629)(605,628)(606,630)
(607,626)(608,625)(609,627)(610,623)(611,622)(612,624)(613,620)(614,619)
(615,621);
s1 := Sym(738)!(  1,496)(  2,498)(  3,497)(  4,493)(  5,495)(  6,494)(  7,613)
(  8,615)(  9,614)( 10,610)( 11,612)( 12,611)( 13,607)( 14,609)( 15,608)
( 16,604)( 17,606)( 18,605)( 19,601)( 20,603)( 21,602)( 22,598)( 23,600)
( 24,599)( 25,595)( 26,597)( 27,596)( 28,592)( 29,594)( 30,593)( 31,589)
( 32,591)( 33,590)( 34,586)( 35,588)( 36,587)( 37,583)( 38,585)( 39,584)
( 40,580)( 41,582)( 42,581)( 43,577)( 44,579)( 45,578)( 46,574)( 47,576)
( 48,575)( 49,571)( 50,573)( 51,572)( 52,568)( 53,570)( 54,569)( 55,565)
( 56,567)( 57,566)( 58,562)( 59,564)( 60,563)( 61,559)( 62,561)( 63,560)
( 64,556)( 65,558)( 66,557)( 67,553)( 68,555)( 69,554)( 70,550)( 71,552)
( 72,551)( 73,547)( 74,549)( 75,548)( 76,544)( 77,546)( 78,545)( 79,541)
( 80,543)( 81,542)( 82,538)( 83,540)( 84,539)( 85,535)( 86,537)( 87,536)
( 88,532)( 89,534)( 90,533)( 91,529)( 92,531)( 93,530)( 94,526)( 95,528)
( 96,527)( 97,523)( 98,525)( 99,524)(100,520)(101,522)(102,521)(103,517)
(104,519)(105,518)(106,514)(107,516)(108,515)(109,511)(110,513)(111,512)
(112,508)(113,510)(114,509)(115,505)(116,507)(117,506)(118,502)(119,504)
(120,503)(121,499)(122,501)(123,500)(124,373)(125,375)(126,374)(127,370)
(128,372)(129,371)(130,490)(131,492)(132,491)(133,487)(134,489)(135,488)
(136,484)(137,486)(138,485)(139,481)(140,483)(141,482)(142,478)(143,480)
(144,479)(145,475)(146,477)(147,476)(148,472)(149,474)(150,473)(151,469)
(152,471)(153,470)(154,466)(155,468)(156,467)(157,463)(158,465)(159,464)
(160,460)(161,462)(162,461)(163,457)(164,459)(165,458)(166,454)(167,456)
(168,455)(169,451)(170,453)(171,452)(172,448)(173,450)(174,449)(175,445)
(176,447)(177,446)(178,442)(179,444)(180,443)(181,439)(182,441)(183,440)
(184,436)(185,438)(186,437)(187,433)(188,435)(189,434)(190,430)(191,432)
(192,431)(193,427)(194,429)(195,428)(196,424)(197,426)(198,425)(199,421)
(200,423)(201,422)(202,418)(203,420)(204,419)(205,415)(206,417)(207,416)
(208,412)(209,414)(210,413)(211,409)(212,411)(213,410)(214,406)(215,408)
(216,407)(217,403)(218,405)(219,404)(220,400)(221,402)(222,401)(223,397)
(224,399)(225,398)(226,394)(227,396)(228,395)(229,391)(230,393)(231,392)
(232,388)(233,390)(234,389)(235,385)(236,387)(237,386)(238,382)(239,384)
(240,383)(241,379)(242,381)(243,380)(244,376)(245,378)(246,377)(247,620)
(248,619)(249,621)(250,617)(251,616)(252,618)(253,737)(254,736)(255,738)
(256,734)(257,733)(258,735)(259,731)(260,730)(261,732)(262,728)(263,727)
(264,729)(265,725)(266,724)(267,726)(268,722)(269,721)(270,723)(271,719)
(272,718)(273,720)(274,716)(275,715)(276,717)(277,713)(278,712)(279,714)
(280,710)(281,709)(282,711)(283,707)(284,706)(285,708)(286,704)(287,703)
(288,705)(289,701)(290,700)(291,702)(292,698)(293,697)(294,699)(295,695)
(296,694)(297,696)(298,692)(299,691)(300,693)(301,689)(302,688)(303,690)
(304,686)(305,685)(306,687)(307,683)(308,682)(309,684)(310,680)(311,679)
(312,681)(313,677)(314,676)(315,678)(316,674)(317,673)(318,675)(319,671)
(320,670)(321,672)(322,668)(323,667)(324,669)(325,665)(326,664)(327,666)
(328,662)(329,661)(330,663)(331,659)(332,658)(333,660)(334,656)(335,655)
(336,657)(337,653)(338,652)(339,654)(340,650)(341,649)(342,651)(343,647)
(344,646)(345,648)(346,644)(347,643)(348,645)(349,641)(350,640)(351,642)
(352,638)(353,637)(354,639)(355,635)(356,634)(357,636)(358,632)(359,631)
(360,633)(361,629)(362,628)(363,630)(364,626)(365,625)(366,627)(367,623)
(368,622)(369,624);
poly := sub<Sym(738)|s0,s1>;

Finitely Presented Group Representation (Magma) :

poly<s0,s1> := Group< s0,s1 | s0*s0, s1*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;

References : None.
to this polytope