Polytope of Type {586}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {586}*1172
Also Known As : 586-gon, {586}. if this polytope has another name.
Group : SmallGroup(1172,4)
Rank : 2
Schlafli Type : {586}
Number of vertices, edges, etc : 586, 586
Order of s₀s₁ : 586
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 : {293}*586
   293-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope