Polytope of Type {608}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {608}*1216
Also Known As : 608-gon, {608}. if this polytope has another name.
Group : SmallGroup(1216,385)
Rank : 2
Schlafli Type : {608}
Number of vertices, edges, etc : 608, 608
Order of s₀s₁ : 608
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 : {304}*608
   4-fold quotients : {152}*304
   8-fold quotients : {76}*152
   16-fold quotients : {38}*76
   19-fold quotients : {32}*64
   32-fold quotients : {19}*38
   38-fold quotients : {16}*32
   76-fold quotients : {8}*16
   152-fold quotients : {4}*8
   304-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope