Polytope of Type {690}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {690}*1380
Also Known As : 690-gon, {690}. if this polytope has another name.
Group : SmallGroup(1380,28)
Rank : 2
Schlafli Type : {690}
Number of vertices, edges, etc : 690, 690
Order of s₀s₁ : 690
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 : {345}*690
   3-fold quotients : {230}*460
   5-fold quotients : {138}*276
   6-fold quotients : {115}*230
   10-fold quotients : {69}*138
   15-fold quotients : {46}*92
   23-fold quotients : {30}*60
   30-fold quotients : {23}*46
   46-fold quotients : {15}*30
   69-fold quotients : {10}*20
   115-fold quotients : {6}*12
   138-fold quotients : {5}*10
   230-fold quotients : {3}*6
   345-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := (  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)(  9, 16)
( 10, 15)( 11, 14)( 12, 13)( 24, 93)( 25,115)( 26,114)( 27,113)( 28,112)
( 29,111)( 30,110)( 31,109)( 32,108)( 33,107)( 34,106)( 35,105)( 36,104)
( 37,103)( 38,102)( 39,101)( 40,100)( 41, 99)( 42, 98)( 43, 97)( 44, 96)
( 45, 95)( 46, 94)( 47, 70)( 48, 92)( 49, 91)( 50, 90)( 51, 89)( 52, 88)
( 53, 87)( 54, 86)( 55, 85)( 56, 84)( 57, 83)( 58, 82)( 59, 81)( 60, 80)
( 61, 79)( 62, 78)( 63, 77)( 64, 76)( 65, 75)( 66, 74)( 67, 73)( 68, 72)
( 69, 71)(116,231)(117,253)(118,252)(119,251)(120,250)(121,249)(122,248)
(123,247)(124,246)(125,245)(126,244)(127,243)(128,242)(129,241)(130,240)
(131,239)(132,238)(133,237)(134,236)(135,235)(136,234)(137,233)(138,232)
(139,323)(140,345)(141,344)(142,343)(143,342)(144,341)(145,340)(146,339)
(147,338)(148,337)(149,336)(150,335)(151,334)(152,333)(153,332)(154,331)
(155,330)(156,329)(157,328)(158,327)(159,326)(160,325)(161,324)(162,300)
(163,322)(164,321)(165,320)(166,319)(167,318)(168,317)(169,316)(170,315)
(171,314)(172,313)(173,312)(174,311)(175,310)(176,309)(177,308)(178,307)
(179,306)(180,305)(181,304)(182,303)(183,302)(184,301)(185,277)(186,299)
(187,298)(188,297)(189,296)(190,295)(191,294)(192,293)(193,292)(194,291)
(195,290)(196,289)(197,288)(198,287)(199,286)(200,285)(201,284)(202,283)
(203,282)(204,281)(205,280)(206,279)(207,278)(208,254)(209,276)(210,275)
(211,274)(212,273)(213,272)(214,271)(215,270)(216,269)(217,268)(218,267)
(219,266)(220,265)(221,264)(222,263)(223,262)(224,261)(225,260)(226,259)
(227,258)(228,257)(229,256)(230,255)(347,368)(348,367)(349,366)(350,365)
(351,364)(352,363)(353,362)(354,361)(355,360)(356,359)(357,358)(369,438)
(370,460)(371,459)(372,458)(373,457)(374,456)(375,455)(376,454)(377,453)
(378,452)(379,451)(380,450)(381,449)(382,448)(383,447)(384,446)(385,445)
(386,444)(387,443)(388,442)(389,441)(390,440)(391,439)(392,415)(393,437)
(394,436)(395,435)(396,434)(397,433)(398,432)(399,431)(400,430)(401,429)
(402,428)(403,427)(404,426)(405,425)(406,424)(407,423)(408,422)(409,421)
(410,420)(411,419)(412,418)(413,417)(414,416)(461,576)(462,598)(463,597)
(464,596)(465,595)(466,594)(467,593)(468,592)(469,591)(470,590)(471,589)
(472,588)(473,587)(474,586)(475,585)(476,584)(477,583)(478,582)(479,581)
(480,580)(481,579)(482,578)(483,577)(484,668)(485,690)(486,689)(487,688)
(488,687)(489,686)(490,685)(491,684)(492,683)(493,682)(494,681)(495,680)
(496,679)(497,678)(498,677)(499,676)(500,675)(501,674)(502,673)(503,672)
(504,671)(505,670)(506,669)(507,645)(508,667)(509,666)(510,665)(511,664)
(512,663)(513,662)(514,661)(515,660)(516,659)(517,658)(518,657)(519,656)
(520,655)(521,654)(522,653)(523,652)(524,651)(525,650)(526,649)(527,648)
(528,647)(529,646)(530,622)(531,644)(532,643)(533,642)(534,641)(535,640)
(536,639)(537,638)(538,637)(539,636)(540,635)(541,634)(542,633)(543,632)
(544,631)(545,630)(546,629)(547,628)(548,627)(549,626)(550,625)(551,624)
(552,623)(553,599)(554,621)(555,620)(556,619)(557,618)(558,617)(559,616)
(560,615)(561,614)(562,613)(563,612)(564,611)(565,610)(566,609)(567,608)
(568,607)(569,606)(570,605)(571,604)(572,603)(573,602)(574,601)(575,600);;
s1 := (  1,485)(  2,484)(  3,506)(  4,505)(  5,504)(  6,503)(  7,502)(  8,501)
(  9,500)( 10,499)( 11,498)( 12,497)( 13,496)( 14,495)( 15,494)( 16,493)
( 17,492)( 18,491)( 19,490)( 20,489)( 21,488)( 22,487)( 23,486)( 24,462)
( 25,461)( 26,483)( 27,482)( 28,481)( 29,480)( 30,479)( 31,478)( 32,477)
( 33,476)( 34,475)( 35,474)( 36,473)( 37,472)( 38,471)( 39,470)( 40,469)
( 41,468)( 42,467)( 43,466)( 44,465)( 45,464)( 46,463)( 47,554)( 48,553)
( 49,575)( 50,574)( 51,573)( 52,572)( 53,571)( 54,570)( 55,569)( 56,568)
( 57,567)( 58,566)( 59,565)( 60,564)( 61,563)( 62,562)( 63,561)( 64,560)
( 65,559)( 66,558)( 67,557)( 68,556)( 69,555)( 70,531)( 71,530)( 72,552)
( 73,551)( 74,550)( 75,549)( 76,548)( 77,547)( 78,546)( 79,545)( 80,544)
( 81,543)( 82,542)( 83,541)( 84,540)( 85,539)( 86,538)( 87,537)( 88,536)
( 89,535)( 90,534)( 91,533)( 92,532)( 93,508)( 94,507)( 95,529)( 96,528)
( 97,527)( 98,526)( 99,525)(100,524)(101,523)(102,522)(103,521)(104,520)
(105,519)(106,518)(107,517)(108,516)(109,515)(110,514)(111,513)(112,512)
(113,511)(114,510)(115,509)(116,370)(117,369)(118,391)(119,390)(120,389)
(121,388)(122,387)(123,386)(124,385)(125,384)(126,383)(127,382)(128,381)
(129,380)(130,379)(131,378)(132,377)(133,376)(134,375)(135,374)(136,373)
(137,372)(138,371)(139,347)(140,346)(141,368)(142,367)(143,366)(144,365)
(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)(152,357)
(153,356)(154,355)(155,354)(156,353)(157,352)(158,351)(159,350)(160,349)
(161,348)(162,439)(163,438)(164,460)(165,459)(166,458)(167,457)(168,456)
(169,455)(170,454)(171,453)(172,452)(173,451)(174,450)(175,449)(176,448)
(177,447)(178,446)(179,445)(180,444)(181,443)(182,442)(183,441)(184,440)
(185,416)(186,415)(187,437)(188,436)(189,435)(190,434)(191,433)(192,432)
(193,431)(194,430)(195,429)(196,428)(197,427)(198,426)(199,425)(200,424)
(201,423)(202,422)(203,421)(204,420)(205,419)(206,418)(207,417)(208,393)
(209,392)(210,414)(211,413)(212,412)(213,411)(214,410)(215,409)(216,408)
(217,407)(218,406)(219,405)(220,404)(221,403)(222,402)(223,401)(224,400)
(225,399)(226,398)(227,397)(228,396)(229,395)(230,394)(231,600)(232,599)
(233,621)(234,620)(235,619)(236,618)(237,617)(238,616)(239,615)(240,614)
(241,613)(242,612)(243,611)(244,610)(245,609)(246,608)(247,607)(248,606)
(249,605)(250,604)(251,603)(252,602)(253,601)(254,577)(255,576)(256,598)
(257,597)(258,596)(259,595)(260,594)(261,593)(262,592)(263,591)(264,590)
(265,589)(266,588)(267,587)(268,586)(269,585)(270,584)(271,583)(272,582)
(273,581)(274,580)(275,579)(276,578)(277,669)(278,668)(279,690)(280,689)
(281,688)(282,687)(283,686)(284,685)(285,684)(286,683)(287,682)(288,681)
(289,680)(290,679)(291,678)(292,677)(293,676)(294,675)(295,674)(296,673)
(297,672)(298,671)(299,670)(300,646)(301,645)(302,667)(303,666)(304,665)
(305,664)(306,663)(307,662)(308,661)(309,660)(310,659)(311,658)(312,657)
(313,656)(314,655)(315,654)(316,653)(317,652)(318,651)(319,650)(320,649)
(321,648)(322,647)(323,623)(324,622)(325,644)(326,643)(327,642)(328,641)
(329,640)(330,639)(331,638)(332,637)(333,636)(334,635)(335,634)(336,633)
(337,632)(338,631)(339,630)(340,629)(341,628)(342,627)(343,626)(344,625)
(345,624);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(690)!(  2, 23)(  3, 22)(  4, 21)(  5, 20)(  6, 19)(  7, 18)(  8, 17)
(  9, 16)( 10, 15)( 11, 14)( 12, 13)( 24, 93)( 25,115)( 26,114)( 27,113)
( 28,112)( 29,111)( 30,110)( 31,109)( 32,108)( 33,107)( 34,106)( 35,105)
( 36,104)( 37,103)( 38,102)( 39,101)( 40,100)( 41, 99)( 42, 98)( 43, 97)
( 44, 96)( 45, 95)( 46, 94)( 47, 70)( 48, 92)( 49, 91)( 50, 90)( 51, 89)
( 52, 88)( 53, 87)( 54, 86)( 55, 85)( 56, 84)( 57, 83)( 58, 82)( 59, 81)
( 60, 80)( 61, 79)( 62, 78)( 63, 77)( 64, 76)( 65, 75)( 66, 74)( 67, 73)
( 68, 72)( 69, 71)(116,231)(117,253)(118,252)(119,251)(120,250)(121,249)
(122,248)(123,247)(124,246)(125,245)(126,244)(127,243)(128,242)(129,241)
(130,240)(131,239)(132,238)(133,237)(134,236)(135,235)(136,234)(137,233)
(138,232)(139,323)(140,345)(141,344)(142,343)(143,342)(144,341)(145,340)
(146,339)(147,338)(148,337)(149,336)(150,335)(151,334)(152,333)(153,332)
(154,331)(155,330)(156,329)(157,328)(158,327)(159,326)(160,325)(161,324)
(162,300)(163,322)(164,321)(165,320)(166,319)(167,318)(168,317)(169,316)
(170,315)(171,314)(172,313)(173,312)(174,311)(175,310)(176,309)(177,308)
(178,307)(179,306)(180,305)(181,304)(182,303)(183,302)(184,301)(185,277)
(186,299)(187,298)(188,297)(189,296)(190,295)(191,294)(192,293)(193,292)
(194,291)(195,290)(196,289)(197,288)(198,287)(199,286)(200,285)(201,284)
(202,283)(203,282)(204,281)(205,280)(206,279)(207,278)(208,254)(209,276)
(210,275)(211,274)(212,273)(213,272)(214,271)(215,270)(216,269)(217,268)
(218,267)(219,266)(220,265)(221,264)(222,263)(223,262)(224,261)(225,260)
(226,259)(227,258)(228,257)(229,256)(230,255)(347,368)(348,367)(349,366)
(350,365)(351,364)(352,363)(353,362)(354,361)(355,360)(356,359)(357,358)
(369,438)(370,460)(371,459)(372,458)(373,457)(374,456)(375,455)(376,454)
(377,453)(378,452)(379,451)(380,450)(381,449)(382,448)(383,447)(384,446)
(385,445)(386,444)(387,443)(388,442)(389,441)(390,440)(391,439)(392,415)
(393,437)(394,436)(395,435)(396,434)(397,433)(398,432)(399,431)(400,430)
(401,429)(402,428)(403,427)(404,426)(405,425)(406,424)(407,423)(408,422)
(409,421)(410,420)(411,419)(412,418)(413,417)(414,416)(461,576)(462,598)
(463,597)(464,596)(465,595)(466,594)(467,593)(468,592)(469,591)(470,590)
(471,589)(472,588)(473,587)(474,586)(475,585)(476,584)(477,583)(478,582)
(479,581)(480,580)(481,579)(482,578)(483,577)(484,668)(485,690)(486,689)
(487,688)(488,687)(489,686)(490,685)(491,684)(492,683)(493,682)(494,681)
(495,680)(496,679)(497,678)(498,677)(499,676)(500,675)(501,674)(502,673)
(503,672)(504,671)(505,670)(506,669)(507,645)(508,667)(509,666)(510,665)
(511,664)(512,663)(513,662)(514,661)(515,660)(516,659)(517,658)(518,657)
(519,656)(520,655)(521,654)(522,653)(523,652)(524,651)(525,650)(526,649)
(527,648)(528,647)(529,646)(530,622)(531,644)(532,643)(533,642)(534,641)
(535,640)(536,639)(537,638)(538,637)(539,636)(540,635)(541,634)(542,633)
(543,632)(544,631)(545,630)(546,629)(547,628)(548,627)(549,626)(550,625)
(551,624)(552,623)(553,599)(554,621)(555,620)(556,619)(557,618)(558,617)
(559,616)(560,615)(561,614)(562,613)(563,612)(564,611)(565,610)(566,609)
(567,608)(568,607)(569,606)(570,605)(571,604)(572,603)(573,602)(574,601)
(575,600);
s1 := Sym(690)!(  1,485)(  2,484)(  3,506)(  4,505)(  5,504)(  6,503)(  7,502)
(  8,501)(  9,500)( 10,499)( 11,498)( 12,497)( 13,496)( 14,495)( 15,494)
( 16,493)( 17,492)( 18,491)( 19,490)( 20,489)( 21,488)( 22,487)( 23,486)
( 24,462)( 25,461)( 26,483)( 27,482)( 28,481)( 29,480)( 30,479)( 31,478)
( 32,477)( 33,476)( 34,475)( 35,474)( 36,473)( 37,472)( 38,471)( 39,470)
( 40,469)( 41,468)( 42,467)( 43,466)( 44,465)( 45,464)( 46,463)( 47,554)
( 48,553)( 49,575)( 50,574)( 51,573)( 52,572)( 53,571)( 54,570)( 55,569)
( 56,568)( 57,567)( 58,566)( 59,565)( 60,564)( 61,563)( 62,562)( 63,561)
( 64,560)( 65,559)( 66,558)( 67,557)( 68,556)( 69,555)( 70,531)( 71,530)
( 72,552)( 73,551)( 74,550)( 75,549)( 76,548)( 77,547)( 78,546)( 79,545)
( 80,544)( 81,543)( 82,542)( 83,541)( 84,540)( 85,539)( 86,538)( 87,537)
( 88,536)( 89,535)( 90,534)( 91,533)( 92,532)( 93,508)( 94,507)( 95,529)
( 96,528)( 97,527)( 98,526)( 99,525)(100,524)(101,523)(102,522)(103,521)
(104,520)(105,519)(106,518)(107,517)(108,516)(109,515)(110,514)(111,513)
(112,512)(113,511)(114,510)(115,509)(116,370)(117,369)(118,391)(119,390)
(120,389)(121,388)(122,387)(123,386)(124,385)(125,384)(126,383)(127,382)
(128,381)(129,380)(130,379)(131,378)(132,377)(133,376)(134,375)(135,374)
(136,373)(137,372)(138,371)(139,347)(140,346)(141,368)(142,367)(143,366)
(144,365)(145,364)(146,363)(147,362)(148,361)(149,360)(150,359)(151,358)
(152,357)(153,356)(154,355)(155,354)(156,353)(157,352)(158,351)(159,350)
(160,349)(161,348)(162,439)(163,438)(164,460)(165,459)(166,458)(167,457)
(168,456)(169,455)(170,454)(171,453)(172,452)(173,451)(174,450)(175,449)
(176,448)(177,447)(178,446)(179,445)(180,444)(181,443)(182,442)(183,441)
(184,440)(185,416)(186,415)(187,437)(188,436)(189,435)(190,434)(191,433)
(192,432)(193,431)(194,430)(195,429)(196,428)(197,427)(198,426)(199,425)
(200,424)(201,423)(202,422)(203,421)(204,420)(205,419)(206,418)(207,417)
(208,393)(209,392)(210,414)(211,413)(212,412)(213,411)(214,410)(215,409)
(216,408)(217,407)(218,406)(219,405)(220,404)(221,403)(222,402)(223,401)
(224,400)(225,399)(226,398)(227,397)(228,396)(229,395)(230,394)(231,600)
(232,599)(233,621)(234,620)(235,619)(236,618)(237,617)(238,616)(239,615)
(240,614)(241,613)(242,612)(243,611)(244,610)(245,609)(246,608)(247,607)
(248,606)(249,605)(250,604)(251,603)(252,602)(253,601)(254,577)(255,576)
(256,598)(257,597)(258,596)(259,595)(260,594)(261,593)(262,592)(263,591)
(264,590)(265,589)(266,588)(267,587)(268,586)(269,585)(270,584)(271,583)
(272,582)(273,581)(274,580)(275,579)(276,578)(277,669)(278,668)(279,690)
(280,689)(281,688)(282,687)(283,686)(284,685)(285,684)(286,683)(287,682)
(288,681)(289,680)(290,679)(291,678)(292,677)(293,676)(294,675)(295,674)
(296,673)(297,672)(298,671)(299,670)(300,646)(301,645)(302,667)(303,666)
(304,665)(305,664)(306,663)(307,662)(308,661)(309,660)(310,659)(311,658)
(312,657)(313,656)(314,655)(315,654)(316,653)(317,652)(318,651)(319,650)
(320,649)(321,648)(322,647)(323,623)(324,622)(325,644)(326,643)(327,642)
(328,641)(329,640)(330,639)(331,638)(332,637)(333,636)(334,635)(335,634)
(336,633)(337,632)(338,631)(339,630)(340,629)(341,628)(342,627)(343,626)
(344,625)(345,624);
poly := sub<Sym(690)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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