Polytope of Type {658}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {658}*1316
Also Known As : 658-gon, {658}. if this polytope has another name.
Group : SmallGroup(1316,8)
Rank : 2
Schlafli Type : {658}
Number of vertices, edges, etc : 658, 658
Order of s₀s₁ : 658
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 : {329}*658
   7-fold quotients : {94}*188
   14-fold quotients : {47}*94
   47-fold quotients : {14}*28
   94-fold quotients : {7}*14
   329-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope