Polytope of Type {610}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {610}*1220
Also Known As : 610-gon, {610}. if this polytope has another name.
Group : SmallGroup(1220,19)
Rank : 2
Schlafli Type : {610}
Number of vertices, edges, etc : 610, 610
Order of s₀s₁ : 610
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 : {305}*610
   5-fold quotients : {122}*244
   10-fold quotients : {61}*122
   61-fold quotients : {10}*20
   122-fold quotients : {5}*10
   305-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)(  9, 54)
( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)( 17, 46)
( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)( 25, 38)
( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 62,245)( 63,305)
( 64,304)( 65,303)( 66,302)( 67,301)( 68,300)( 69,299)( 70,298)( 71,297)
( 72,296)( 73,295)( 74,294)( 75,293)( 76,292)( 77,291)( 78,290)( 79,289)
( 80,288)( 81,287)( 82,286)( 83,285)( 84,284)( 85,283)( 86,282)( 87,281)
( 88,280)( 89,279)( 90,278)( 91,277)( 92,276)( 93,275)( 94,274)( 95,273)
( 96,272)( 97,271)( 98,270)( 99,269)(100,268)(101,267)(102,266)(103,265)
(104,264)(105,263)(106,262)(107,261)(108,260)(109,259)(110,258)(111,257)
(112,256)(113,255)(114,254)(115,253)(116,252)(117,251)(118,250)(119,249)
(120,248)(121,247)(122,246)(123,184)(124,244)(125,243)(126,242)(127,241)
(128,240)(129,239)(130,238)(131,237)(132,236)(133,235)(134,234)(135,233)
(136,232)(137,231)(138,230)(139,229)(140,228)(141,227)(142,226)(143,225)
(144,224)(145,223)(146,222)(147,221)(148,220)(149,219)(150,218)(151,217)
(152,216)(153,215)(154,214)(155,213)(156,212)(157,211)(158,210)(159,209)
(160,208)(161,207)(162,206)(163,205)(164,204)(165,203)(166,202)(167,201)
(168,200)(169,199)(170,198)(171,197)(172,196)(173,195)(174,194)(175,193)
(176,192)(177,191)(178,190)(179,189)(180,188)(181,187)(182,186)(183,185)
(307,366)(308,365)(309,364)(310,363)(311,362)(312,361)(313,360)(314,359)
(315,358)(316,357)(317,356)(318,355)(319,354)(320,353)(321,352)(322,351)
(323,350)(324,349)(325,348)(326,347)(327,346)(328,345)(329,344)(330,343)
(331,342)(332,341)(333,340)(334,339)(335,338)(336,337)(367,550)(368,610)
(369,609)(370,608)(371,607)(372,606)(373,605)(374,604)(375,603)(376,602)
(377,601)(378,600)(379,599)(380,598)(381,597)(382,596)(383,595)(384,594)
(385,593)(386,592)(387,591)(388,590)(389,589)(390,588)(391,587)(392,586)
(393,585)(394,584)(395,583)(396,582)(397,581)(398,580)(399,579)(400,578)
(401,577)(402,576)(403,575)(404,574)(405,573)(406,572)(407,571)(408,570)
(409,569)(410,568)(411,567)(412,566)(413,565)(414,564)(415,563)(416,562)
(417,561)(418,560)(419,559)(420,558)(421,557)(422,556)(423,555)(424,554)
(425,553)(426,552)(427,551)(428,489)(429,549)(430,548)(431,547)(432,546)
(433,545)(434,544)(435,543)(436,542)(437,541)(438,540)(439,539)(440,538)
(441,537)(442,536)(443,535)(444,534)(445,533)(446,532)(447,531)(448,530)
(449,529)(450,528)(451,527)(452,526)(453,525)(454,524)(455,523)(456,522)
(457,521)(458,520)(459,519)(460,518)(461,517)(462,516)(463,515)(464,514)
(465,513)(466,512)(467,511)(468,510)(469,509)(470,508)(471,507)(472,506)
(473,505)(474,504)(475,503)(476,502)(477,501)(478,500)(479,499)(480,498)
(481,497)(482,496)(483,495)(484,494)(485,493)(486,492)(487,491)(488,490);;
s1 := (  1,368)(  2,367)(  3,427)(  4,426)(  5,425)(  6,424)(  7,423)(  8,422)
(  9,421)( 10,420)( 11,419)( 12,418)( 13,417)( 14,416)( 15,415)( 16,414)
( 17,413)( 18,412)( 19,411)( 20,410)( 21,409)( 22,408)( 23,407)( 24,406)
( 25,405)( 26,404)( 27,403)( 28,402)( 29,401)( 30,400)( 31,399)( 32,398)
( 33,397)( 34,396)( 35,395)( 36,394)( 37,393)( 38,392)( 39,391)( 40,390)
( 41,389)( 42,388)( 43,387)( 44,386)( 45,385)( 46,384)( 47,383)( 48,382)
( 49,381)( 50,380)( 51,379)( 52,378)( 53,377)( 54,376)( 55,375)( 56,374)
( 57,373)( 58,372)( 59,371)( 60,370)( 61,369)( 62,307)( 63,306)( 64,366)
( 65,365)( 66,364)( 67,363)( 68,362)( 69,361)( 70,360)( 71,359)( 72,358)
( 73,357)( 74,356)( 75,355)( 76,354)( 77,353)( 78,352)( 79,351)( 80,350)
( 81,349)( 82,348)( 83,347)( 84,346)( 85,345)( 86,344)( 87,343)( 88,342)
( 89,341)( 90,340)( 91,339)( 92,338)( 93,337)( 94,336)( 95,335)( 96,334)
( 97,333)( 98,332)( 99,331)(100,330)(101,329)(102,328)(103,327)(104,326)
(105,325)(106,324)(107,323)(108,322)(109,321)(110,320)(111,319)(112,318)
(113,317)(114,316)(115,315)(116,314)(117,313)(118,312)(119,311)(120,310)
(121,309)(122,308)(123,551)(124,550)(125,610)(126,609)(127,608)(128,607)
(129,606)(130,605)(131,604)(132,603)(133,602)(134,601)(135,600)(136,599)
(137,598)(138,597)(139,596)(140,595)(141,594)(142,593)(143,592)(144,591)
(145,590)(146,589)(147,588)(148,587)(149,586)(150,585)(151,584)(152,583)
(153,582)(154,581)(155,580)(156,579)(157,578)(158,577)(159,576)(160,575)
(161,574)(162,573)(163,572)(164,571)(165,570)(166,569)(167,568)(168,567)
(169,566)(170,565)(171,564)(172,563)(173,562)(174,561)(175,560)(176,559)
(177,558)(178,557)(179,556)(180,555)(181,554)(182,553)(183,552)(184,490)
(185,489)(186,549)(187,548)(188,547)(189,546)(190,545)(191,544)(192,543)
(193,542)(194,541)(195,540)(196,539)(197,538)(198,537)(199,536)(200,535)
(201,534)(202,533)(203,532)(204,531)(205,530)(206,529)(207,528)(208,527)
(209,526)(210,525)(211,524)(212,523)(213,522)(214,521)(215,520)(216,519)
(217,518)(218,517)(219,516)(220,515)(221,514)(222,513)(223,512)(224,511)
(225,510)(226,509)(227,508)(228,507)(229,506)(230,505)(231,504)(232,503)
(233,502)(234,501)(235,500)(236,499)(237,498)(238,497)(239,496)(240,495)
(241,494)(242,493)(243,492)(244,491)(245,429)(246,428)(247,488)(248,487)
(249,486)(250,485)(251,484)(252,483)(253,482)(254,481)(255,480)(256,479)
(257,478)(258,477)(259,476)(260,475)(261,474)(262,473)(263,472)(264,471)
(265,470)(266,469)(267,468)(268,467)(269,466)(270,465)(271,464)(272,463)
(273,462)(274,461)(275,460)(276,459)(277,458)(278,457)(279,456)(280,455)
(281,454)(282,453)(283,452)(284,451)(285,450)(286,449)(287,448)(288,447)
(289,446)(290,445)(291,444)(292,443)(293,442)(294,441)(295,440)(296,439)
(297,438)(298,437)(299,436)(300,435)(301,434)(302,433)(303,432)(304,431)
(305,430);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(610)!(  2, 61)(  3, 60)(  4, 59)(  5, 58)(  6, 57)(  7, 56)(  8, 55)
(  9, 54)( 10, 53)( 11, 52)( 12, 51)( 13, 50)( 14, 49)( 15, 48)( 16, 47)
( 17, 46)( 18, 45)( 19, 44)( 20, 43)( 21, 42)( 22, 41)( 23, 40)( 24, 39)
( 25, 38)( 26, 37)( 27, 36)( 28, 35)( 29, 34)( 30, 33)( 31, 32)( 62,245)
( 63,305)( 64,304)( 65,303)( 66,302)( 67,301)( 68,300)( 69,299)( 70,298)
( 71,297)( 72,296)( 73,295)( 74,294)( 75,293)( 76,292)( 77,291)( 78,290)
( 79,289)( 80,288)( 81,287)( 82,286)( 83,285)( 84,284)( 85,283)( 86,282)
( 87,281)( 88,280)( 89,279)( 90,278)( 91,277)( 92,276)( 93,275)( 94,274)
( 95,273)( 96,272)( 97,271)( 98,270)( 99,269)(100,268)(101,267)(102,266)
(103,265)(104,264)(105,263)(106,262)(107,261)(108,260)(109,259)(110,258)
(111,257)(112,256)(113,255)(114,254)(115,253)(116,252)(117,251)(118,250)
(119,249)(120,248)(121,247)(122,246)(123,184)(124,244)(125,243)(126,242)
(127,241)(128,240)(129,239)(130,238)(131,237)(132,236)(133,235)(134,234)
(135,233)(136,232)(137,231)(138,230)(139,229)(140,228)(141,227)(142,226)
(143,225)(144,224)(145,223)(146,222)(147,221)(148,220)(149,219)(150,218)
(151,217)(152,216)(153,215)(154,214)(155,213)(156,212)(157,211)(158,210)
(159,209)(160,208)(161,207)(162,206)(163,205)(164,204)(165,203)(166,202)
(167,201)(168,200)(169,199)(170,198)(171,197)(172,196)(173,195)(174,194)
(175,193)(176,192)(177,191)(178,190)(179,189)(180,188)(181,187)(182,186)
(183,185)(307,366)(308,365)(309,364)(310,363)(311,362)(312,361)(313,360)
(314,359)(315,358)(316,357)(317,356)(318,355)(319,354)(320,353)(321,352)
(322,351)(323,350)(324,349)(325,348)(326,347)(327,346)(328,345)(329,344)
(330,343)(331,342)(332,341)(333,340)(334,339)(335,338)(336,337)(367,550)
(368,610)(369,609)(370,608)(371,607)(372,606)(373,605)(374,604)(375,603)
(376,602)(377,601)(378,600)(379,599)(380,598)(381,597)(382,596)(383,595)
(384,594)(385,593)(386,592)(387,591)(388,590)(389,589)(390,588)(391,587)
(392,586)(393,585)(394,584)(395,583)(396,582)(397,581)(398,580)(399,579)
(400,578)(401,577)(402,576)(403,575)(404,574)(405,573)(406,572)(407,571)
(408,570)(409,569)(410,568)(411,567)(412,566)(413,565)(414,564)(415,563)
(416,562)(417,561)(418,560)(419,559)(420,558)(421,557)(422,556)(423,555)
(424,554)(425,553)(426,552)(427,551)(428,489)(429,549)(430,548)(431,547)
(432,546)(433,545)(434,544)(435,543)(436,542)(437,541)(438,540)(439,539)
(440,538)(441,537)(442,536)(443,535)(444,534)(445,533)(446,532)(447,531)
(448,530)(449,529)(450,528)(451,527)(452,526)(453,525)(454,524)(455,523)
(456,522)(457,521)(458,520)(459,519)(460,518)(461,517)(462,516)(463,515)
(464,514)(465,513)(466,512)(467,511)(468,510)(469,509)(470,508)(471,507)
(472,506)(473,505)(474,504)(475,503)(476,502)(477,501)(478,500)(479,499)
(480,498)(481,497)(482,496)(483,495)(484,494)(485,493)(486,492)(487,491)
(488,490);
s1 := Sym(610)!(  1,368)(  2,367)(  3,427)(  4,426)(  5,425)(  6,424)(  7,423)
(  8,422)(  9,421)( 10,420)( 11,419)( 12,418)( 13,417)( 14,416)( 15,415)
( 16,414)( 17,413)( 18,412)( 19,411)( 20,410)( 21,409)( 22,408)( 23,407)
( 24,406)( 25,405)( 26,404)( 27,403)( 28,402)( 29,401)( 30,400)( 31,399)
( 32,398)( 33,397)( 34,396)( 35,395)( 36,394)( 37,393)( 38,392)( 39,391)
( 40,390)( 41,389)( 42,388)( 43,387)( 44,386)( 45,385)( 46,384)( 47,383)
( 48,382)( 49,381)( 50,380)( 51,379)( 52,378)( 53,377)( 54,376)( 55,375)
( 56,374)( 57,373)( 58,372)( 59,371)( 60,370)( 61,369)( 62,307)( 63,306)
( 64,366)( 65,365)( 66,364)( 67,363)( 68,362)( 69,361)( 70,360)( 71,359)
( 72,358)( 73,357)( 74,356)( 75,355)( 76,354)( 77,353)( 78,352)( 79,351)
( 80,350)( 81,349)( 82,348)( 83,347)( 84,346)( 85,345)( 86,344)( 87,343)
( 88,342)( 89,341)( 90,340)( 91,339)( 92,338)( 93,337)( 94,336)( 95,335)
( 96,334)( 97,333)( 98,332)( 99,331)(100,330)(101,329)(102,328)(103,327)
(104,326)(105,325)(106,324)(107,323)(108,322)(109,321)(110,320)(111,319)
(112,318)(113,317)(114,316)(115,315)(116,314)(117,313)(118,312)(119,311)
(120,310)(121,309)(122,308)(123,551)(124,550)(125,610)(126,609)(127,608)
(128,607)(129,606)(130,605)(131,604)(132,603)(133,602)(134,601)(135,600)
(136,599)(137,598)(138,597)(139,596)(140,595)(141,594)(142,593)(143,592)
(144,591)(145,590)(146,589)(147,588)(148,587)(149,586)(150,585)(151,584)
(152,583)(153,582)(154,581)(155,580)(156,579)(157,578)(158,577)(159,576)
(160,575)(161,574)(162,573)(163,572)(164,571)(165,570)(166,569)(167,568)
(168,567)(169,566)(170,565)(171,564)(172,563)(173,562)(174,561)(175,560)
(176,559)(177,558)(178,557)(179,556)(180,555)(181,554)(182,553)(183,552)
(184,490)(185,489)(186,549)(187,548)(188,547)(189,546)(190,545)(191,544)
(192,543)(193,542)(194,541)(195,540)(196,539)(197,538)(198,537)(199,536)
(200,535)(201,534)(202,533)(203,532)(204,531)(205,530)(206,529)(207,528)
(208,527)(209,526)(210,525)(211,524)(212,523)(213,522)(214,521)(215,520)
(216,519)(217,518)(218,517)(219,516)(220,515)(221,514)(222,513)(223,512)
(224,511)(225,510)(226,509)(227,508)(228,507)(229,506)(230,505)(231,504)
(232,503)(233,502)(234,501)(235,500)(236,499)(237,498)(238,497)(239,496)
(240,495)(241,494)(242,493)(243,492)(244,491)(245,429)(246,428)(247,488)
(248,487)(249,486)(250,485)(251,484)(252,483)(253,482)(254,481)(255,480)
(256,479)(257,478)(258,477)(259,476)(260,475)(261,474)(262,473)(263,472)
(264,471)(265,470)(266,469)(267,468)(268,467)(269,466)(270,465)(271,464)
(272,463)(273,462)(274,461)(275,460)(276,459)(277,458)(278,457)(279,456)
(280,455)(281,454)(282,453)(283,452)(284,451)(285,450)(286,449)(287,448)
(288,447)(289,446)(290,445)(291,444)(292,443)(293,442)(294,441)(295,440)
(296,439)(297,438)(298,437)(299,436)(300,435)(301,434)(302,433)(303,432)
(304,431)(305,430);
poly := sub<Sym(610)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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