Polytope of Type {654}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {654}*1308
Also Known As : 654-gon, {654}. if this polytope has another name.
Group : SmallGroup(1308,17)
Rank : 2
Schlafli Type : {654}
Number of vertices, edges, etc : 654, 654
Order of s₀s₁ : 654
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 : {327}*654
   3-fold quotients : {218}*436
   6-fold quotients : {109}*218
   109-fold quotients : {6}*12
   218-fold quotients : {3}*6
   327-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope