Polytope of Type {656}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {656}*1312
Also Known As : 656-gon, {656}. if this polytope has another name.
Group : SmallGroup(1312,88)
Rank : 2
Schlafli Type : {656}
Number of vertices, edges, etc : 656, 656
Order of s₀s₁ : 656
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 : {328}*656
   4-fold quotients : {164}*328
   8-fold quotients : {82}*164
   16-fold quotients : {41}*82
   41-fold quotients : {16}*32
   82-fold quotients : {8}*16
   164-fold quotients : {4}*8
   328-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope