Polytope of Type {4,166}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,166}*1328
Also Known As : {4,166|2}. if this polytope has another name.
Group : SmallGroup(1328,34)
Rank : 3
Schlafli Type : {4,166}
Number of vertices, edges, etc : 4, 332, 166
Order of s0s1s2 : 332
Order of s0s1s2s1 : 2
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Flat
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 : {2,166}*664
4-fold quotients : {2,83}*332
83-fold quotients : {4,2}*16
166-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := (333,416)(334,417)(335,418)(336,419)(337,420)(338,421)(339,422)(340,423)
(341,424)(342,425)(343,426)(344,427)(345,428)(346,429)(347,430)(348,431)
(349,432)(350,433)(351,434)(352,435)(353,436)(354,437)(355,438)(356,439)
(357,440)(358,441)(359,442)(360,443)(361,444)(362,445)(363,446)(364,447)
(365,448)(366,449)(367,450)(368,451)(369,452)(370,453)(371,454)(372,455)
(373,456)(374,457)(375,458)(376,459)(377,460)(378,461)(379,462)(380,463)
(381,464)(382,465)(383,466)(384,467)(385,468)(386,469)(387,470)(388,471)
(389,472)(390,473)(391,474)(392,475)(393,476)(394,477)(395,478)(396,479)
(397,480)(398,481)(399,482)(400,483)(401,484)(402,485)(403,486)(404,487)
(405,488)(406,489)(407,490)(408,491)(409,492)(410,493)(411,494)(412,495)
(413,496)(414,497)(415,498)(499,582)(500,583)(501,584)(502,585)(503,586)
(504,587)(505,588)(506,589)(507,590)(508,591)(509,592)(510,593)(511,594)
(512,595)(513,596)(514,597)(515,598)(516,599)(517,600)(518,601)(519,602)
(520,603)(521,604)(522,605)(523,606)(524,607)(525,608)(526,609)(527,610)
(528,611)(529,612)(530,613)(531,614)(532,615)(533,616)(534,617)(535,618)
(536,619)(537,620)(538,621)(539,622)(540,623)(541,624)(542,625)(543,626)
(544,627)(545,628)(546,629)(547,630)(548,631)(549,632)(550,633)(551,634)
(552,635)(553,636)(554,637)(555,638)(556,639)(557,640)(558,641)(559,642)
(560,643)(561,644)(562,645)(563,646)(564,647)(565,648)(566,649)(567,650)
(568,651)(569,652)(570,653)(571,654)(572,655)(573,656)(574,657)(575,658)
(576,659)(577,660)(578,661)(579,662)(580,663)(581,664);;
s1 := ( 1,499)( 2,581)( 3,580)( 4,579)( 5,578)( 6,577)( 7,576)( 8,575)
( 9,574)( 10,573)( 11,572)( 12,571)( 13,570)( 14,569)( 15,568)( 16,567)
( 17,566)( 18,565)( 19,564)( 20,563)( 21,562)( 22,561)( 23,560)( 24,559)
( 25,558)( 26,557)( 27,556)( 28,555)( 29,554)( 30,553)( 31,552)( 32,551)
( 33,550)( 34,549)( 35,548)( 36,547)( 37,546)( 38,545)( 39,544)( 40,543)
( 41,542)( 42,541)( 43,540)( 44,539)( 45,538)( 46,537)( 47,536)( 48,535)
( 49,534)( 50,533)( 51,532)( 52,531)( 53,530)( 54,529)( 55,528)( 56,527)
( 57,526)( 58,525)( 59,524)( 60,523)( 61,522)( 62,521)( 63,520)( 64,519)
( 65,518)( 66,517)( 67,516)( 68,515)( 69,514)( 70,513)( 71,512)( 72,511)
( 73,510)( 74,509)( 75,508)( 76,507)( 77,506)( 78,505)( 79,504)( 80,503)
( 81,502)( 82,501)( 83,500)( 84,582)( 85,664)( 86,663)( 87,662)( 88,661)
( 89,660)( 90,659)( 91,658)( 92,657)( 93,656)( 94,655)( 95,654)( 96,653)
( 97,652)( 98,651)( 99,650)(100,649)(101,648)(102,647)(103,646)(104,645)
(105,644)(106,643)(107,642)(108,641)(109,640)(110,639)(111,638)(112,637)
(113,636)(114,635)(115,634)(116,633)(117,632)(118,631)(119,630)(120,629)
(121,628)(122,627)(123,626)(124,625)(125,624)(126,623)(127,622)(128,621)
(129,620)(130,619)(131,618)(132,617)(133,616)(134,615)(135,614)(136,613)
(137,612)(138,611)(139,610)(140,609)(141,608)(142,607)(143,606)(144,605)
(145,604)(146,603)(147,602)(148,601)(149,600)(150,599)(151,598)(152,597)
(153,596)(154,595)(155,594)(156,593)(157,592)(158,591)(159,590)(160,589)
(161,588)(162,587)(163,586)(164,585)(165,584)(166,583)(167,333)(168,415)
(169,414)(170,413)(171,412)(172,411)(173,410)(174,409)(175,408)(176,407)
(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,400)(184,399)
(185,398)(186,397)(187,396)(188,395)(189,394)(190,393)(191,392)(192,391)
(193,390)(194,389)(195,388)(196,387)(197,386)(198,385)(199,384)(200,383)
(201,382)(202,381)(203,380)(204,379)(205,378)(206,377)(207,376)(208,375)
(209,374)(210,373)(211,372)(212,371)(213,370)(214,369)(215,368)(216,367)
(217,366)(218,365)(219,364)(220,363)(221,362)(222,361)(223,360)(224,359)
(225,358)(226,357)(227,356)(228,355)(229,354)(230,353)(231,352)(232,351)
(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,344)(240,343)
(241,342)(242,341)(243,340)(244,339)(245,338)(246,337)(247,336)(248,335)
(249,334)(250,416)(251,498)(252,497)(253,496)(254,495)(255,494)(256,493)
(257,492)(258,491)(259,490)(260,489)(261,488)(262,487)(263,486)(264,485)
(265,484)(266,483)(267,482)(268,481)(269,480)(270,479)(271,478)(272,477)
(273,476)(274,475)(275,474)(276,473)(277,472)(278,471)(279,470)(280,469)
(281,468)(282,467)(283,466)(284,465)(285,464)(286,463)(287,462)(288,461)
(289,460)(290,459)(291,458)(292,457)(293,456)(294,455)(295,454)(296,453)
(297,452)(298,451)(299,450)(300,449)(301,448)(302,447)(303,446)(304,445)
(305,444)(306,443)(307,442)(308,441)(309,440)(310,439)(311,438)(312,437)
(313,436)(314,435)(315,434)(316,433)(317,432)(318,431)(319,430)(320,429)
(321,428)(322,427)(323,426)(324,425)(325,424)(326,423)(327,422)(328,421)
(329,420)(330,419)(331,418)(332,417);;
s2 := ( 1,168)( 2,167)( 3,249)( 4,248)( 5,247)( 6,246)( 7,245)( 8,244)
( 9,243)( 10,242)( 11,241)( 12,240)( 13,239)( 14,238)( 15,237)( 16,236)
( 17,235)( 18,234)( 19,233)( 20,232)( 21,231)( 22,230)( 23,229)( 24,228)
( 25,227)( 26,226)( 27,225)( 28,224)( 29,223)( 30,222)( 31,221)( 32,220)
( 33,219)( 34,218)( 35,217)( 36,216)( 37,215)( 38,214)( 39,213)( 40,212)
( 41,211)( 42,210)( 43,209)( 44,208)( 45,207)( 46,206)( 47,205)( 48,204)
( 49,203)( 50,202)( 51,201)( 52,200)( 53,199)( 54,198)( 55,197)( 56,196)
( 57,195)( 58,194)( 59,193)( 60,192)( 61,191)( 62,190)( 63,189)( 64,188)
( 65,187)( 66,186)( 67,185)( 68,184)( 69,183)( 70,182)( 71,181)( 72,180)
( 73,179)( 74,178)( 75,177)( 76,176)( 77,175)( 78,174)( 79,173)( 80,172)
( 81,171)( 82,170)( 83,169)( 84,251)( 85,250)( 86,332)( 87,331)( 88,330)
( 89,329)( 90,328)( 91,327)( 92,326)( 93,325)( 94,324)( 95,323)( 96,322)
( 97,321)( 98,320)( 99,319)(100,318)(101,317)(102,316)(103,315)(104,314)
(105,313)(106,312)(107,311)(108,310)(109,309)(110,308)(111,307)(112,306)
(113,305)(114,304)(115,303)(116,302)(117,301)(118,300)(119,299)(120,298)
(121,297)(122,296)(123,295)(124,294)(125,293)(126,292)(127,291)(128,290)
(129,289)(130,288)(131,287)(132,286)(133,285)(134,284)(135,283)(136,282)
(137,281)(138,280)(139,279)(140,278)(141,277)(142,276)(143,275)(144,274)
(145,273)(146,272)(147,271)(148,270)(149,269)(150,268)(151,267)(152,266)
(153,265)(154,264)(155,263)(156,262)(157,261)(158,260)(159,259)(160,258)
(161,257)(162,256)(163,255)(164,254)(165,253)(166,252)(333,500)(334,499)
(335,581)(336,580)(337,579)(338,578)(339,577)(340,576)(341,575)(342,574)
(343,573)(344,572)(345,571)(346,570)(347,569)(348,568)(349,567)(350,566)
(351,565)(352,564)(353,563)(354,562)(355,561)(356,560)(357,559)(358,558)
(359,557)(360,556)(361,555)(362,554)(363,553)(364,552)(365,551)(366,550)
(367,549)(368,548)(369,547)(370,546)(371,545)(372,544)(373,543)(374,542)
(375,541)(376,540)(377,539)(378,538)(379,537)(380,536)(381,535)(382,534)
(383,533)(384,532)(385,531)(386,530)(387,529)(388,528)(389,527)(390,526)
(391,525)(392,524)(393,523)(394,522)(395,521)(396,520)(397,519)(398,518)
(399,517)(400,516)(401,515)(402,514)(403,513)(404,512)(405,511)(406,510)
(407,509)(408,508)(409,507)(410,506)(411,505)(412,504)(413,503)(414,502)
(415,501)(416,583)(417,582)(418,664)(419,663)(420,662)(421,661)(422,660)
(423,659)(424,658)(425,657)(426,656)(427,655)(428,654)(429,653)(430,652)
(431,651)(432,650)(433,649)(434,648)(435,647)(436,646)(437,645)(438,644)
(439,643)(440,642)(441,641)(442,640)(443,639)(444,638)(445,637)(446,636)
(447,635)(448,634)(449,633)(450,632)(451,631)(452,630)(453,629)(454,628)
(455,627)(456,626)(457,625)(458,624)(459,623)(460,622)(461,621)(462,620)
(463,619)(464,618)(465,617)(466,616)(467,615)(468,614)(469,613)(470,612)
(471,611)(472,610)(473,609)(474,608)(475,607)(476,606)(477,605)(478,604)
(479,603)(480,602)(481,601)(482,600)(483,599)(484,598)(485,597)(486,596)
(487,595)(488,594)(489,593)(490,592)(491,591)(492,590)(493,589)(494,588)
(495,587)(496,586)(497,585)(498,584);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) :
F := FreeGroup("s0","s1","s2");;
s0 := F.1;; s1 := F.2;; s2 := F.3;;
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(664)!(333,416)(334,417)(335,418)(336,419)(337,420)(338,421)(339,422)
(340,423)(341,424)(342,425)(343,426)(344,427)(345,428)(346,429)(347,430)
(348,431)(349,432)(350,433)(351,434)(352,435)(353,436)(354,437)(355,438)
(356,439)(357,440)(358,441)(359,442)(360,443)(361,444)(362,445)(363,446)
(364,447)(365,448)(366,449)(367,450)(368,451)(369,452)(370,453)(371,454)
(372,455)(373,456)(374,457)(375,458)(376,459)(377,460)(378,461)(379,462)
(380,463)(381,464)(382,465)(383,466)(384,467)(385,468)(386,469)(387,470)
(388,471)(389,472)(390,473)(391,474)(392,475)(393,476)(394,477)(395,478)
(396,479)(397,480)(398,481)(399,482)(400,483)(401,484)(402,485)(403,486)
(404,487)(405,488)(406,489)(407,490)(408,491)(409,492)(410,493)(411,494)
(412,495)(413,496)(414,497)(415,498)(499,582)(500,583)(501,584)(502,585)
(503,586)(504,587)(505,588)(506,589)(507,590)(508,591)(509,592)(510,593)
(511,594)(512,595)(513,596)(514,597)(515,598)(516,599)(517,600)(518,601)
(519,602)(520,603)(521,604)(522,605)(523,606)(524,607)(525,608)(526,609)
(527,610)(528,611)(529,612)(530,613)(531,614)(532,615)(533,616)(534,617)
(535,618)(536,619)(537,620)(538,621)(539,622)(540,623)(541,624)(542,625)
(543,626)(544,627)(545,628)(546,629)(547,630)(548,631)(549,632)(550,633)
(551,634)(552,635)(553,636)(554,637)(555,638)(556,639)(557,640)(558,641)
(559,642)(560,643)(561,644)(562,645)(563,646)(564,647)(565,648)(566,649)
(567,650)(568,651)(569,652)(570,653)(571,654)(572,655)(573,656)(574,657)
(575,658)(576,659)(577,660)(578,661)(579,662)(580,663)(581,664);
s1 := Sym(664)!( 1,499)( 2,581)( 3,580)( 4,579)( 5,578)( 6,577)( 7,576)
( 8,575)( 9,574)( 10,573)( 11,572)( 12,571)( 13,570)( 14,569)( 15,568)
( 16,567)( 17,566)( 18,565)( 19,564)( 20,563)( 21,562)( 22,561)( 23,560)
( 24,559)( 25,558)( 26,557)( 27,556)( 28,555)( 29,554)( 30,553)( 31,552)
( 32,551)( 33,550)( 34,549)( 35,548)( 36,547)( 37,546)( 38,545)( 39,544)
( 40,543)( 41,542)( 42,541)( 43,540)( 44,539)( 45,538)( 46,537)( 47,536)
( 48,535)( 49,534)( 50,533)( 51,532)( 52,531)( 53,530)( 54,529)( 55,528)
( 56,527)( 57,526)( 58,525)( 59,524)( 60,523)( 61,522)( 62,521)( 63,520)
( 64,519)( 65,518)( 66,517)( 67,516)( 68,515)( 69,514)( 70,513)( 71,512)
( 72,511)( 73,510)( 74,509)( 75,508)( 76,507)( 77,506)( 78,505)( 79,504)
( 80,503)( 81,502)( 82,501)( 83,500)( 84,582)( 85,664)( 86,663)( 87,662)
( 88,661)( 89,660)( 90,659)( 91,658)( 92,657)( 93,656)( 94,655)( 95,654)
( 96,653)( 97,652)( 98,651)( 99,650)(100,649)(101,648)(102,647)(103,646)
(104,645)(105,644)(106,643)(107,642)(108,641)(109,640)(110,639)(111,638)
(112,637)(113,636)(114,635)(115,634)(116,633)(117,632)(118,631)(119,630)
(120,629)(121,628)(122,627)(123,626)(124,625)(125,624)(126,623)(127,622)
(128,621)(129,620)(130,619)(131,618)(132,617)(133,616)(134,615)(135,614)
(136,613)(137,612)(138,611)(139,610)(140,609)(141,608)(142,607)(143,606)
(144,605)(145,604)(146,603)(147,602)(148,601)(149,600)(150,599)(151,598)
(152,597)(153,596)(154,595)(155,594)(156,593)(157,592)(158,591)(159,590)
(160,589)(161,588)(162,587)(163,586)(164,585)(165,584)(166,583)(167,333)
(168,415)(169,414)(170,413)(171,412)(172,411)(173,410)(174,409)(175,408)
(176,407)(177,406)(178,405)(179,404)(180,403)(181,402)(182,401)(183,400)
(184,399)(185,398)(186,397)(187,396)(188,395)(189,394)(190,393)(191,392)
(192,391)(193,390)(194,389)(195,388)(196,387)(197,386)(198,385)(199,384)
(200,383)(201,382)(202,381)(203,380)(204,379)(205,378)(206,377)(207,376)
(208,375)(209,374)(210,373)(211,372)(212,371)(213,370)(214,369)(215,368)
(216,367)(217,366)(218,365)(219,364)(220,363)(221,362)(222,361)(223,360)
(224,359)(225,358)(226,357)(227,356)(228,355)(229,354)(230,353)(231,352)
(232,351)(233,350)(234,349)(235,348)(236,347)(237,346)(238,345)(239,344)
(240,343)(241,342)(242,341)(243,340)(244,339)(245,338)(246,337)(247,336)
(248,335)(249,334)(250,416)(251,498)(252,497)(253,496)(254,495)(255,494)
(256,493)(257,492)(258,491)(259,490)(260,489)(261,488)(262,487)(263,486)
(264,485)(265,484)(266,483)(267,482)(268,481)(269,480)(270,479)(271,478)
(272,477)(273,476)(274,475)(275,474)(276,473)(277,472)(278,471)(279,470)
(280,469)(281,468)(282,467)(283,466)(284,465)(285,464)(286,463)(287,462)
(288,461)(289,460)(290,459)(291,458)(292,457)(293,456)(294,455)(295,454)
(296,453)(297,452)(298,451)(299,450)(300,449)(301,448)(302,447)(303,446)
(304,445)(305,444)(306,443)(307,442)(308,441)(309,440)(310,439)(311,438)
(312,437)(313,436)(314,435)(315,434)(316,433)(317,432)(318,431)(319,430)
(320,429)(321,428)(322,427)(323,426)(324,425)(325,424)(326,423)(327,422)
(328,421)(329,420)(330,419)(331,418)(332,417);
s2 := Sym(664)!( 1,168)( 2,167)( 3,249)( 4,248)( 5,247)( 6,246)( 7,245)
( 8,244)( 9,243)( 10,242)( 11,241)( 12,240)( 13,239)( 14,238)( 15,237)
( 16,236)( 17,235)( 18,234)( 19,233)( 20,232)( 21,231)( 22,230)( 23,229)
( 24,228)( 25,227)( 26,226)( 27,225)( 28,224)( 29,223)( 30,222)( 31,221)
( 32,220)( 33,219)( 34,218)( 35,217)( 36,216)( 37,215)( 38,214)( 39,213)
( 40,212)( 41,211)( 42,210)( 43,209)( 44,208)( 45,207)( 46,206)( 47,205)
( 48,204)( 49,203)( 50,202)( 51,201)( 52,200)( 53,199)( 54,198)( 55,197)
( 56,196)( 57,195)( 58,194)( 59,193)( 60,192)( 61,191)( 62,190)( 63,189)
( 64,188)( 65,187)( 66,186)( 67,185)( 68,184)( 69,183)( 70,182)( 71,181)
( 72,180)( 73,179)( 74,178)( 75,177)( 76,176)( 77,175)( 78,174)( 79,173)
( 80,172)( 81,171)( 82,170)( 83,169)( 84,251)( 85,250)( 86,332)( 87,331)
( 88,330)( 89,329)( 90,328)( 91,327)( 92,326)( 93,325)( 94,324)( 95,323)
( 96,322)( 97,321)( 98,320)( 99,319)(100,318)(101,317)(102,316)(103,315)
(104,314)(105,313)(106,312)(107,311)(108,310)(109,309)(110,308)(111,307)
(112,306)(113,305)(114,304)(115,303)(116,302)(117,301)(118,300)(119,299)
(120,298)(121,297)(122,296)(123,295)(124,294)(125,293)(126,292)(127,291)
(128,290)(129,289)(130,288)(131,287)(132,286)(133,285)(134,284)(135,283)
(136,282)(137,281)(138,280)(139,279)(140,278)(141,277)(142,276)(143,275)
(144,274)(145,273)(146,272)(147,271)(148,270)(149,269)(150,268)(151,267)
(152,266)(153,265)(154,264)(155,263)(156,262)(157,261)(158,260)(159,259)
(160,258)(161,257)(162,256)(163,255)(164,254)(165,253)(166,252)(333,500)
(334,499)(335,581)(336,580)(337,579)(338,578)(339,577)(340,576)(341,575)
(342,574)(343,573)(344,572)(345,571)(346,570)(347,569)(348,568)(349,567)
(350,566)(351,565)(352,564)(353,563)(354,562)(355,561)(356,560)(357,559)
(358,558)(359,557)(360,556)(361,555)(362,554)(363,553)(364,552)(365,551)
(366,550)(367,549)(368,548)(369,547)(370,546)(371,545)(372,544)(373,543)
(374,542)(375,541)(376,540)(377,539)(378,538)(379,537)(380,536)(381,535)
(382,534)(383,533)(384,532)(385,531)(386,530)(387,529)(388,528)(389,527)
(390,526)(391,525)(392,524)(393,523)(394,522)(395,521)(396,520)(397,519)
(398,518)(399,517)(400,516)(401,515)(402,514)(403,513)(404,512)(405,511)
(406,510)(407,509)(408,508)(409,507)(410,506)(411,505)(412,504)(413,503)
(414,502)(415,501)(416,583)(417,582)(418,664)(419,663)(420,662)(421,661)
(422,660)(423,659)(424,658)(425,657)(426,656)(427,655)(428,654)(429,653)
(430,652)(431,651)(432,650)(433,649)(434,648)(435,647)(436,646)(437,645)
(438,644)(439,643)(440,642)(441,641)(442,640)(443,639)(444,638)(445,637)
(446,636)(447,635)(448,634)(449,633)(450,632)(451,631)(452,630)(453,629)
(454,628)(455,627)(456,626)(457,625)(458,624)(459,623)(460,622)(461,621)
(462,620)(463,619)(464,618)(465,617)(466,616)(467,615)(468,614)(469,613)
(470,612)(471,611)(472,610)(473,609)(474,608)(475,607)(476,606)(477,605)
(478,604)(479,603)(480,602)(481,601)(482,600)(483,599)(484,598)(485,597)
(486,596)(487,595)(488,594)(489,593)(490,592)(491,591)(492,590)(493,589)
(494,588)(495,587)(496,586)(497,585)(498,584);
poly := sub<Sym(664)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) :
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2,
s0*s2*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope