Polytope of Type {584}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {584}*1168
Also Known As : 584-gon, {584}. if this polytope has another name.
Group : SmallGroup(1168,26)
Rank : 2
Schlafli Type : {584}
Number of vertices, edges, etc : 584, 584
Order of s₀s₁ : 584
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 : {292}*584
   4-fold quotients : {146}*292
   8-fold quotients : {73}*146
   73-fold quotients : {8}*16
   146-fold quotients : {4}*8
   292-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope