Polytope of Type {624}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {624}*1248
Also Known As : 624-gon, {624}. if this polytope has another name.
Group : SmallGroup(1248,224)
Rank : 2
Schlafli Type : {624}
Number of vertices, edges, etc : 624, 624
Order of s₀s₁ : 624
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 : {312}*624
   3-fold quotients : {208}*416
   4-fold quotients : {156}*312
   6-fold quotients : {104}*208
   8-fold quotients : {78}*156
   12-fold quotients : {52}*104
   13-fold quotients : {48}*96
   16-fold quotients : {39}*78
   24-fold quotients : {26}*52
   26-fold quotients : {24}*48
   39-fold quotients : {16}*32
   48-fold quotients : {13}*26
   52-fold quotients : {12}*24
   78-fold quotients : {8}*16
   104-fold quotients : {6}*12
   156-fold quotients : {4}*8
   208-fold quotients : {3}*6
   312-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope