Polytope of Type {660}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {660}*1320
Also Known As : 660-gon, {660}. if this polytope has another name.
Group : SmallGroup(1320,127)
Rank : 2
Schlafli Type : {660}
Number of vertices, edges, etc : 660, 660
Order of s₀s₁ : 660
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 : {330}*660
   3-fold quotients : {220}*440
   4-fold quotients : {165}*330
   5-fold quotients : {132}*264
   6-fold quotients : {110}*220
   10-fold quotients : {66}*132
   11-fold quotients : {60}*120
   12-fold quotients : {55}*110
   15-fold quotients : {44}*88
   20-fold quotients : {33}*66
   22-fold quotients : {30}*60
   30-fold quotients : {22}*44
   33-fold quotients : {20}*40
   44-fold quotients : {15}*30
   55-fold quotients : {12}*24
   60-fold quotients : {11}*22
   66-fold quotients : {10}*20
   110-fold quotients : {6}*12
   132-fold quotients : {5}*10
   165-fold quotients : {4}*8
   220-fold quotients : {3}*6
   330-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope