Polytope of Type {736}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {736}*1472
Also Known As : 736-gon, {736}. if this polytope has another name.
Group : SmallGroup(1472,385)
Rank : 2
Schlafli Type : {736}
Number of vertices, edges, etc : 736, 736
Order of s₀s₁ : 736
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 : {368}*736
   4-fold quotients : {184}*368
   8-fold quotients : {92}*184
   16-fold quotients : {46}*92
   23-fold quotients : {32}*64
   32-fold quotients : {23}*46
   46-fold quotients : {16}*32
   92-fold quotients : {8}*16
   184-fold quotients : {4}*8
   368-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope