Polytope of Type {580}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {580}*1160
Also Known As : 580-gon, {580}. if this polytope has another name.
Group : SmallGroup(1160,30)
Rank : 2
Schlafli Type : {580}
Number of vertices, edges, etc : 580, 580
Order of s₀s₁ : 580
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 : {290}*580
   4-fold quotients : {145}*290
   5-fold quotients : {116}*232
   10-fold quotients : {58}*116
   20-fold quotients : {29}*58
   29-fold quotients : {20}*40
   58-fold quotients : {10}*20
   116-fold quotients : {5}*10
   145-fold quotients : {4}*8
   290-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope