Polytope of Type {648}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {648}*1296
Also Known As : 648-gon, {648}. if this polytope has another name.
Group : SmallGroup(1296,8)
Rank : 2
Schlafli Type : {648}
Number of vertices, edges, etc : 648, 648
Order of s₀s₁ : 648
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 : {324}*648
   3-fold quotients : {216}*432
   4-fold quotients : {162}*324
   6-fold quotients : {108}*216
   8-fold quotients : {81}*162
   9-fold quotients : {72}*144
   12-fold quotients : {54}*108
   18-fold quotients : {36}*72
   24-fold quotients : {27}*54
   27-fold quotients : {24}*48
   36-fold quotients : {18}*36
   54-fold quotients : {12}*24
   72-fold quotients : {9}*18
   81-fold quotients : {8}*16
   108-fold quotients : {6}*12
   162-fold quotients : {4}*8
   216-fold quotients : {3}*6
   324-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope