Polytope of Type {590}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {590}*1180
Also Known As : 590-gon, {590}. if this polytope has another name.
Group : SmallGroup(1180,10)
Rank : 2
Schlafli Type : {590}
Number of vertices, edges, etc : 590, 590
Order of s₀s₁ : 590
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 : {295}*590
   5-fold quotients : {118}*236
   10-fold quotients : {59}*118
   59-fold quotients : {10}*20
   118-fold quotients : {5}*10
   295-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope