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.
Irregular Quotients (of which this is a minimal cover):
None.
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