Polytope of Type {616}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {616}*1232
Also Known As : 616-gon, {616}. if this polytope has another name.
Group : SmallGroup(1232,65)
Rank : 2
Schlafli Type : {616}
Number of vertices, edges, etc : 616, 616
Order of s₀s₁ : 616
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 : {308}*616
   4-fold quotients : {154}*308
   7-fold quotients : {88}*176
   8-fold quotients : {77}*154
   11-fold quotients : {56}*112
   14-fold quotients : {44}*88
   22-fold quotients : {28}*56
   28-fold quotients : {22}*44
   44-fold quotients : {14}*28
   56-fold quotients : {11}*22
   77-fold quotients : {8}*16
   88-fold quotients : {7}*14
   154-fold quotients : {4}*8
   308-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope