Polytope of Type {664}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {664}*1328
Also Known As : 664-gon, {664}. if this polytope has another name.
Group : SmallGroup(1328,26)
Rank : 2
Schlafli Type : {664}
Number of vertices, edges, etc : 664, 664
Order of s₀s₁ : 664
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 : {332}*664
   4-fold quotients : {166}*332
   8-fold quotients : {83}*166
   83-fold quotients : {8}*16
   166-fold quotients : {4}*8
   332-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope