Polytope of Type {588}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {588}*1176
Also Known As : 588-gon, {588}. if this polytope has another name.
Group : SmallGroup(1176,36)
Rank : 2
Schlafli Type : {588}
Number of vertices, edges, etc : 588, 588
Order of s₀s₁ : 588
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 : {294}*588
   3-fold quotients : {196}*392
   4-fold quotients : {147}*294
   6-fold quotients : {98}*196
   7-fold quotients : {84}*168
   12-fold quotients : {49}*98
   14-fold quotients : {42}*84
   21-fold quotients : {28}*56
   28-fold quotients : {21}*42
   42-fold quotients : {14}*28
   49-fold quotients : {12}*24
   84-fold quotients : {7}*14
   98-fold quotients : {6}*12
   147-fold quotients : {4}*8
   196-fold quotients : {3}*6
   294-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope