Polytope of Type {582}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {582}*1164
Also Known As : 582-gon, {582}. if this polytope has another name.
Group : SmallGroup(1164,17)
Rank : 2
Schlafli Type : {582}
Number of vertices, edges, etc : 582, 582
Order of s₀s₁ : 582
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 : {291}*582
   3-fold quotients : {194}*388
   6-fold quotients : {97}*194
   97-fold quotients : {6}*12
   194-fold quotients : {3}*6
   291-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope