Polytope of Type {4,84}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,84}*1344b
if this polytope has a name.
Group : SmallGroup(1344,11397)
Rank : 3
Schlafli Type : {4,84}
Number of vertices, edges, etc : 8, 336, 168
Order of s0s1s2 : 84
Order of s0s1s2s1 : 4
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
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 : {4,84}*672b, {4,84}*672c, {4,42}*672
4-fold quotients : {2,84}*336, {4,21}*336, {4,42}*336b, {4,42}*336c
7-fold quotients : {4,12}*192b
8-fold quotients : {4,21}*168, {2,42}*168
12-fold quotients : {2,28}*112
14-fold quotients : {4,12}*96b, {4,12}*96c, {4,6}*96
16-fold quotients : {2,21}*84
24-fold quotients : {2,14}*56
28-fold quotients : {2,12}*48, {4,3}*48, {4,6}*48b, {4,6}*48c
48-fold quotients : {2,7}*28
56-fold quotients : {4,3}*24, {2,6}*24
84-fold quotients : {2,4}*16
112-fold quotients : {2,3}*12
168-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,339)( 2,340)( 3,337)( 4,338)( 5,343)( 6,344)( 7,341)( 8,342)
( 9,347)( 10,348)( 11,345)( 12,346)( 13,351)( 14,352)( 15,349)( 16,350)
( 17,355)( 18,356)( 19,353)( 20,354)( 21,359)( 22,360)( 23,357)( 24,358)
( 25,363)( 26,364)( 27,361)( 28,362)( 29,367)( 30,368)( 31,365)( 32,366)
( 33,371)( 34,372)( 35,369)( 36,370)( 37,375)( 38,376)( 39,373)( 40,374)
( 41,379)( 42,380)( 43,377)( 44,378)( 45,383)( 46,384)( 47,381)( 48,382)
( 49,387)( 50,388)( 51,385)( 52,386)( 53,391)( 54,392)( 55,389)( 56,390)
( 57,395)( 58,396)( 59,393)( 60,394)( 61,399)( 62,400)( 63,397)( 64,398)
( 65,403)( 66,404)( 67,401)( 68,402)( 69,407)( 70,408)( 71,405)( 72,406)
( 73,411)( 74,412)( 75,409)( 76,410)( 77,415)( 78,416)( 79,413)( 80,414)
( 81,419)( 82,420)( 83,417)( 84,418)( 85,423)( 86,424)( 87,421)( 88,422)
( 89,427)( 90,428)( 91,425)( 92,426)( 93,431)( 94,432)( 95,429)( 96,430)
( 97,435)( 98,436)( 99,433)(100,434)(101,439)(102,440)(103,437)(104,438)
(105,443)(106,444)(107,441)(108,442)(109,447)(110,448)(111,445)(112,446)
(113,451)(114,452)(115,449)(116,450)(117,455)(118,456)(119,453)(120,454)
(121,459)(122,460)(123,457)(124,458)(125,463)(126,464)(127,461)(128,462)
(129,467)(130,468)(131,465)(132,466)(133,471)(134,472)(135,469)(136,470)
(137,475)(138,476)(139,473)(140,474)(141,479)(142,480)(143,477)(144,478)
(145,483)(146,484)(147,481)(148,482)(149,487)(150,488)(151,485)(152,486)
(153,491)(154,492)(155,489)(156,490)(157,495)(158,496)(159,493)(160,494)
(161,499)(162,500)(163,497)(164,498)(165,503)(166,504)(167,501)(168,502)
(169,507)(170,508)(171,505)(172,506)(173,511)(174,512)(175,509)(176,510)
(177,515)(178,516)(179,513)(180,514)(181,519)(182,520)(183,517)(184,518)
(185,523)(186,524)(187,521)(188,522)(189,527)(190,528)(191,525)(192,526)
(193,531)(194,532)(195,529)(196,530)(197,535)(198,536)(199,533)(200,534)
(201,539)(202,540)(203,537)(204,538)(205,543)(206,544)(207,541)(208,542)
(209,547)(210,548)(211,545)(212,546)(213,551)(214,552)(215,549)(216,550)
(217,555)(218,556)(219,553)(220,554)(221,559)(222,560)(223,557)(224,558)
(225,563)(226,564)(227,561)(228,562)(229,567)(230,568)(231,565)(232,566)
(233,571)(234,572)(235,569)(236,570)(237,575)(238,576)(239,573)(240,574)
(241,579)(242,580)(243,577)(244,578)(245,583)(246,584)(247,581)(248,582)
(249,587)(250,588)(251,585)(252,586)(253,591)(254,592)(255,589)(256,590)
(257,595)(258,596)(259,593)(260,594)(261,599)(262,600)(263,597)(264,598)
(265,603)(266,604)(267,601)(268,602)(269,607)(270,608)(271,605)(272,606)
(273,611)(274,612)(275,609)(276,610)(277,615)(278,616)(279,613)(280,614)
(281,619)(282,620)(283,617)(284,618)(285,623)(286,624)(287,621)(288,622)
(289,627)(290,628)(291,625)(292,626)(293,631)(294,632)(295,629)(296,630)
(297,635)(298,636)(299,633)(300,634)(301,639)(302,640)(303,637)(304,638)
(305,643)(306,644)(307,641)(308,642)(309,647)(310,648)(311,645)(312,646)
(313,651)(314,652)(315,649)(316,650)(317,655)(318,656)(319,653)(320,654)
(321,659)(322,660)(323,657)(324,658)(325,663)(326,664)(327,661)(328,662)
(329,667)(330,668)(331,665)(332,666)(333,671)(334,672)(335,669)(336,670);;
s1 := ( 3, 4)( 5, 25)( 6, 26)( 7, 28)( 8, 27)( 9, 21)( 10, 22)( 11, 24)
( 12, 23)( 13, 17)( 14, 18)( 15, 20)( 16, 19)( 29, 57)( 30, 58)( 31, 60)
( 32, 59)( 33, 81)( 34, 82)( 35, 84)( 36, 83)( 37, 77)( 38, 78)( 39, 80)
( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)( 47, 72)
( 48, 71)( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)( 55, 64)
( 56, 63)( 87, 88)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)( 94,106)
( 95,108)( 96,107)( 97,101)( 98,102)( 99,104)(100,103)(113,141)(114,142)
(115,144)(116,143)(117,165)(118,166)(119,168)(120,167)(121,161)(122,162)
(123,164)(124,163)(125,157)(126,158)(127,160)(128,159)(129,153)(130,154)
(131,156)(132,155)(133,149)(134,150)(135,152)(136,151)(137,145)(138,146)
(139,148)(140,147)(169,253)(170,254)(171,256)(172,255)(173,277)(174,278)
(175,280)(176,279)(177,273)(178,274)(179,276)(180,275)(181,269)(182,270)
(183,272)(184,271)(185,265)(186,266)(187,268)(188,267)(189,261)(190,262)
(191,264)(192,263)(193,257)(194,258)(195,260)(196,259)(197,309)(198,310)
(199,312)(200,311)(201,333)(202,334)(203,336)(204,335)(205,329)(206,330)
(207,332)(208,331)(209,325)(210,326)(211,328)(212,327)(213,321)(214,322)
(215,324)(216,323)(217,317)(218,318)(219,320)(220,319)(221,313)(222,314)
(223,316)(224,315)(225,281)(226,282)(227,284)(228,283)(229,305)(230,306)
(231,308)(232,307)(233,301)(234,302)(235,304)(236,303)(237,297)(238,298)
(239,300)(240,299)(241,293)(242,294)(243,296)(244,295)(245,289)(246,290)
(247,292)(248,291)(249,285)(250,286)(251,288)(252,287)(339,340)(341,361)
(342,362)(343,364)(344,363)(345,357)(346,358)(347,360)(348,359)(349,353)
(350,354)(351,356)(352,355)(365,393)(366,394)(367,396)(368,395)(369,417)
(370,418)(371,420)(372,419)(373,413)(374,414)(375,416)(376,415)(377,409)
(378,410)(379,412)(380,411)(381,405)(382,406)(383,408)(384,407)(385,401)
(386,402)(387,404)(388,403)(389,397)(390,398)(391,400)(392,399)(423,424)
(425,445)(426,446)(427,448)(428,447)(429,441)(430,442)(431,444)(432,443)
(433,437)(434,438)(435,440)(436,439)(449,477)(450,478)(451,480)(452,479)
(453,501)(454,502)(455,504)(456,503)(457,497)(458,498)(459,500)(460,499)
(461,493)(462,494)(463,496)(464,495)(465,489)(466,490)(467,492)(468,491)
(469,485)(470,486)(471,488)(472,487)(473,481)(474,482)(475,484)(476,483)
(505,589)(506,590)(507,592)(508,591)(509,613)(510,614)(511,616)(512,615)
(513,609)(514,610)(515,612)(516,611)(517,605)(518,606)(519,608)(520,607)
(521,601)(522,602)(523,604)(524,603)(525,597)(526,598)(527,600)(528,599)
(529,593)(530,594)(531,596)(532,595)(533,645)(534,646)(535,648)(536,647)
(537,669)(538,670)(539,672)(540,671)(541,665)(542,666)(543,668)(544,667)
(545,661)(546,662)(547,664)(548,663)(549,657)(550,658)(551,660)(552,659)
(553,653)(554,654)(555,656)(556,655)(557,649)(558,650)(559,652)(560,651)
(561,617)(562,618)(563,620)(564,619)(565,641)(566,642)(567,644)(568,643)
(569,637)(570,638)(571,640)(572,639)(573,633)(574,634)(575,636)(576,635)
(577,629)(578,630)(579,632)(580,631)(581,625)(582,626)(583,628)(584,627)
(585,621)(586,622)(587,624)(588,623);;
s2 := ( 1,201)( 2,204)( 3,203)( 4,202)( 5,197)( 6,200)( 7,199)( 8,198)
( 9,221)( 10,224)( 11,223)( 12,222)( 13,217)( 14,220)( 15,219)( 16,218)
( 17,213)( 18,216)( 19,215)( 20,214)( 21,209)( 22,212)( 23,211)( 24,210)
( 25,205)( 26,208)( 27,207)( 28,206)( 29,173)( 30,176)( 31,175)( 32,174)
( 33,169)( 34,172)( 35,171)( 36,170)( 37,193)( 38,196)( 39,195)( 40,194)
( 41,189)( 42,192)( 43,191)( 44,190)( 45,185)( 46,188)( 47,187)( 48,186)
( 49,181)( 50,184)( 51,183)( 52,182)( 53,177)( 54,180)( 55,179)( 56,178)
( 57,229)( 58,232)( 59,231)( 60,230)( 61,225)( 62,228)( 63,227)( 64,226)
( 65,249)( 66,252)( 67,251)( 68,250)( 69,245)( 70,248)( 71,247)( 72,246)
( 73,241)( 74,244)( 75,243)( 76,242)( 77,237)( 78,240)( 79,239)( 80,238)
( 81,233)( 82,236)( 83,235)( 84,234)( 85,285)( 86,288)( 87,287)( 88,286)
( 89,281)( 90,284)( 91,283)( 92,282)( 93,305)( 94,308)( 95,307)( 96,306)
( 97,301)( 98,304)( 99,303)(100,302)(101,297)(102,300)(103,299)(104,298)
(105,293)(106,296)(107,295)(108,294)(109,289)(110,292)(111,291)(112,290)
(113,257)(114,260)(115,259)(116,258)(117,253)(118,256)(119,255)(120,254)
(121,277)(122,280)(123,279)(124,278)(125,273)(126,276)(127,275)(128,274)
(129,269)(130,272)(131,271)(132,270)(133,265)(134,268)(135,267)(136,266)
(137,261)(138,264)(139,263)(140,262)(141,313)(142,316)(143,315)(144,314)
(145,309)(146,312)(147,311)(148,310)(149,333)(150,336)(151,335)(152,334)
(153,329)(154,332)(155,331)(156,330)(157,325)(158,328)(159,327)(160,326)
(161,321)(162,324)(163,323)(164,322)(165,317)(166,320)(167,319)(168,318)
(337,537)(338,540)(339,539)(340,538)(341,533)(342,536)(343,535)(344,534)
(345,557)(346,560)(347,559)(348,558)(349,553)(350,556)(351,555)(352,554)
(353,549)(354,552)(355,551)(356,550)(357,545)(358,548)(359,547)(360,546)
(361,541)(362,544)(363,543)(364,542)(365,509)(366,512)(367,511)(368,510)
(369,505)(370,508)(371,507)(372,506)(373,529)(374,532)(375,531)(376,530)
(377,525)(378,528)(379,527)(380,526)(381,521)(382,524)(383,523)(384,522)
(385,517)(386,520)(387,519)(388,518)(389,513)(390,516)(391,515)(392,514)
(393,565)(394,568)(395,567)(396,566)(397,561)(398,564)(399,563)(400,562)
(401,585)(402,588)(403,587)(404,586)(405,581)(406,584)(407,583)(408,582)
(409,577)(410,580)(411,579)(412,578)(413,573)(414,576)(415,575)(416,574)
(417,569)(418,572)(419,571)(420,570)(421,621)(422,624)(423,623)(424,622)
(425,617)(426,620)(427,619)(428,618)(429,641)(430,644)(431,643)(432,642)
(433,637)(434,640)(435,639)(436,638)(437,633)(438,636)(439,635)(440,634)
(441,629)(442,632)(443,631)(444,630)(445,625)(446,628)(447,627)(448,626)
(449,593)(450,596)(451,595)(452,594)(453,589)(454,592)(455,591)(456,590)
(457,613)(458,616)(459,615)(460,614)(461,609)(462,612)(463,611)(464,610)
(465,605)(466,608)(467,607)(468,606)(469,601)(470,604)(471,603)(472,602)
(473,597)(474,600)(475,599)(476,598)(477,649)(478,652)(479,651)(480,650)
(481,645)(482,648)(483,647)(484,646)(485,669)(486,672)(487,671)(488,670)
(489,665)(490,668)(491,667)(492,666)(493,661)(494,664)(495,663)(496,662)
(497,657)(498,660)(499,659)(500,658)(501,653)(502,656)(503,655)(504,654);;
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*s2*s1*s0*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(672)!( 1,339)( 2,340)( 3,337)( 4,338)( 5,343)( 6,344)( 7,341)
( 8,342)( 9,347)( 10,348)( 11,345)( 12,346)( 13,351)( 14,352)( 15,349)
( 16,350)( 17,355)( 18,356)( 19,353)( 20,354)( 21,359)( 22,360)( 23,357)
( 24,358)( 25,363)( 26,364)( 27,361)( 28,362)( 29,367)( 30,368)( 31,365)
( 32,366)( 33,371)( 34,372)( 35,369)( 36,370)( 37,375)( 38,376)( 39,373)
( 40,374)( 41,379)( 42,380)( 43,377)( 44,378)( 45,383)( 46,384)( 47,381)
( 48,382)( 49,387)( 50,388)( 51,385)( 52,386)( 53,391)( 54,392)( 55,389)
( 56,390)( 57,395)( 58,396)( 59,393)( 60,394)( 61,399)( 62,400)( 63,397)
( 64,398)( 65,403)( 66,404)( 67,401)( 68,402)( 69,407)( 70,408)( 71,405)
( 72,406)( 73,411)( 74,412)( 75,409)( 76,410)( 77,415)( 78,416)( 79,413)
( 80,414)( 81,419)( 82,420)( 83,417)( 84,418)( 85,423)( 86,424)( 87,421)
( 88,422)( 89,427)( 90,428)( 91,425)( 92,426)( 93,431)( 94,432)( 95,429)
( 96,430)( 97,435)( 98,436)( 99,433)(100,434)(101,439)(102,440)(103,437)
(104,438)(105,443)(106,444)(107,441)(108,442)(109,447)(110,448)(111,445)
(112,446)(113,451)(114,452)(115,449)(116,450)(117,455)(118,456)(119,453)
(120,454)(121,459)(122,460)(123,457)(124,458)(125,463)(126,464)(127,461)
(128,462)(129,467)(130,468)(131,465)(132,466)(133,471)(134,472)(135,469)
(136,470)(137,475)(138,476)(139,473)(140,474)(141,479)(142,480)(143,477)
(144,478)(145,483)(146,484)(147,481)(148,482)(149,487)(150,488)(151,485)
(152,486)(153,491)(154,492)(155,489)(156,490)(157,495)(158,496)(159,493)
(160,494)(161,499)(162,500)(163,497)(164,498)(165,503)(166,504)(167,501)
(168,502)(169,507)(170,508)(171,505)(172,506)(173,511)(174,512)(175,509)
(176,510)(177,515)(178,516)(179,513)(180,514)(181,519)(182,520)(183,517)
(184,518)(185,523)(186,524)(187,521)(188,522)(189,527)(190,528)(191,525)
(192,526)(193,531)(194,532)(195,529)(196,530)(197,535)(198,536)(199,533)
(200,534)(201,539)(202,540)(203,537)(204,538)(205,543)(206,544)(207,541)
(208,542)(209,547)(210,548)(211,545)(212,546)(213,551)(214,552)(215,549)
(216,550)(217,555)(218,556)(219,553)(220,554)(221,559)(222,560)(223,557)
(224,558)(225,563)(226,564)(227,561)(228,562)(229,567)(230,568)(231,565)
(232,566)(233,571)(234,572)(235,569)(236,570)(237,575)(238,576)(239,573)
(240,574)(241,579)(242,580)(243,577)(244,578)(245,583)(246,584)(247,581)
(248,582)(249,587)(250,588)(251,585)(252,586)(253,591)(254,592)(255,589)
(256,590)(257,595)(258,596)(259,593)(260,594)(261,599)(262,600)(263,597)
(264,598)(265,603)(266,604)(267,601)(268,602)(269,607)(270,608)(271,605)
(272,606)(273,611)(274,612)(275,609)(276,610)(277,615)(278,616)(279,613)
(280,614)(281,619)(282,620)(283,617)(284,618)(285,623)(286,624)(287,621)
(288,622)(289,627)(290,628)(291,625)(292,626)(293,631)(294,632)(295,629)
(296,630)(297,635)(298,636)(299,633)(300,634)(301,639)(302,640)(303,637)
(304,638)(305,643)(306,644)(307,641)(308,642)(309,647)(310,648)(311,645)
(312,646)(313,651)(314,652)(315,649)(316,650)(317,655)(318,656)(319,653)
(320,654)(321,659)(322,660)(323,657)(324,658)(325,663)(326,664)(327,661)
(328,662)(329,667)(330,668)(331,665)(332,666)(333,671)(334,672)(335,669)
(336,670);
s1 := Sym(672)!( 3, 4)( 5, 25)( 6, 26)( 7, 28)( 8, 27)( 9, 21)( 10, 22)
( 11, 24)( 12, 23)( 13, 17)( 14, 18)( 15, 20)( 16, 19)( 29, 57)( 30, 58)
( 31, 60)( 32, 59)( 33, 81)( 34, 82)( 35, 84)( 36, 83)( 37, 77)( 38, 78)
( 39, 80)( 40, 79)( 41, 73)( 42, 74)( 43, 76)( 44, 75)( 45, 69)( 46, 70)
( 47, 72)( 48, 71)( 49, 65)( 50, 66)( 51, 68)( 52, 67)( 53, 61)( 54, 62)
( 55, 64)( 56, 63)( 87, 88)( 89,109)( 90,110)( 91,112)( 92,111)( 93,105)
( 94,106)( 95,108)( 96,107)( 97,101)( 98,102)( 99,104)(100,103)(113,141)
(114,142)(115,144)(116,143)(117,165)(118,166)(119,168)(120,167)(121,161)
(122,162)(123,164)(124,163)(125,157)(126,158)(127,160)(128,159)(129,153)
(130,154)(131,156)(132,155)(133,149)(134,150)(135,152)(136,151)(137,145)
(138,146)(139,148)(140,147)(169,253)(170,254)(171,256)(172,255)(173,277)
(174,278)(175,280)(176,279)(177,273)(178,274)(179,276)(180,275)(181,269)
(182,270)(183,272)(184,271)(185,265)(186,266)(187,268)(188,267)(189,261)
(190,262)(191,264)(192,263)(193,257)(194,258)(195,260)(196,259)(197,309)
(198,310)(199,312)(200,311)(201,333)(202,334)(203,336)(204,335)(205,329)
(206,330)(207,332)(208,331)(209,325)(210,326)(211,328)(212,327)(213,321)
(214,322)(215,324)(216,323)(217,317)(218,318)(219,320)(220,319)(221,313)
(222,314)(223,316)(224,315)(225,281)(226,282)(227,284)(228,283)(229,305)
(230,306)(231,308)(232,307)(233,301)(234,302)(235,304)(236,303)(237,297)
(238,298)(239,300)(240,299)(241,293)(242,294)(243,296)(244,295)(245,289)
(246,290)(247,292)(248,291)(249,285)(250,286)(251,288)(252,287)(339,340)
(341,361)(342,362)(343,364)(344,363)(345,357)(346,358)(347,360)(348,359)
(349,353)(350,354)(351,356)(352,355)(365,393)(366,394)(367,396)(368,395)
(369,417)(370,418)(371,420)(372,419)(373,413)(374,414)(375,416)(376,415)
(377,409)(378,410)(379,412)(380,411)(381,405)(382,406)(383,408)(384,407)
(385,401)(386,402)(387,404)(388,403)(389,397)(390,398)(391,400)(392,399)
(423,424)(425,445)(426,446)(427,448)(428,447)(429,441)(430,442)(431,444)
(432,443)(433,437)(434,438)(435,440)(436,439)(449,477)(450,478)(451,480)
(452,479)(453,501)(454,502)(455,504)(456,503)(457,497)(458,498)(459,500)
(460,499)(461,493)(462,494)(463,496)(464,495)(465,489)(466,490)(467,492)
(468,491)(469,485)(470,486)(471,488)(472,487)(473,481)(474,482)(475,484)
(476,483)(505,589)(506,590)(507,592)(508,591)(509,613)(510,614)(511,616)
(512,615)(513,609)(514,610)(515,612)(516,611)(517,605)(518,606)(519,608)
(520,607)(521,601)(522,602)(523,604)(524,603)(525,597)(526,598)(527,600)
(528,599)(529,593)(530,594)(531,596)(532,595)(533,645)(534,646)(535,648)
(536,647)(537,669)(538,670)(539,672)(540,671)(541,665)(542,666)(543,668)
(544,667)(545,661)(546,662)(547,664)(548,663)(549,657)(550,658)(551,660)
(552,659)(553,653)(554,654)(555,656)(556,655)(557,649)(558,650)(559,652)
(560,651)(561,617)(562,618)(563,620)(564,619)(565,641)(566,642)(567,644)
(568,643)(569,637)(570,638)(571,640)(572,639)(573,633)(574,634)(575,636)
(576,635)(577,629)(578,630)(579,632)(580,631)(581,625)(582,626)(583,628)
(584,627)(585,621)(586,622)(587,624)(588,623);
s2 := Sym(672)!( 1,201)( 2,204)( 3,203)( 4,202)( 5,197)( 6,200)( 7,199)
( 8,198)( 9,221)( 10,224)( 11,223)( 12,222)( 13,217)( 14,220)( 15,219)
( 16,218)( 17,213)( 18,216)( 19,215)( 20,214)( 21,209)( 22,212)( 23,211)
( 24,210)( 25,205)( 26,208)( 27,207)( 28,206)( 29,173)( 30,176)( 31,175)
( 32,174)( 33,169)( 34,172)( 35,171)( 36,170)( 37,193)( 38,196)( 39,195)
( 40,194)( 41,189)( 42,192)( 43,191)( 44,190)( 45,185)( 46,188)( 47,187)
( 48,186)( 49,181)( 50,184)( 51,183)( 52,182)( 53,177)( 54,180)( 55,179)
( 56,178)( 57,229)( 58,232)( 59,231)( 60,230)( 61,225)( 62,228)( 63,227)
( 64,226)( 65,249)( 66,252)( 67,251)( 68,250)( 69,245)( 70,248)( 71,247)
( 72,246)( 73,241)( 74,244)( 75,243)( 76,242)( 77,237)( 78,240)( 79,239)
( 80,238)( 81,233)( 82,236)( 83,235)( 84,234)( 85,285)( 86,288)( 87,287)
( 88,286)( 89,281)( 90,284)( 91,283)( 92,282)( 93,305)( 94,308)( 95,307)
( 96,306)( 97,301)( 98,304)( 99,303)(100,302)(101,297)(102,300)(103,299)
(104,298)(105,293)(106,296)(107,295)(108,294)(109,289)(110,292)(111,291)
(112,290)(113,257)(114,260)(115,259)(116,258)(117,253)(118,256)(119,255)
(120,254)(121,277)(122,280)(123,279)(124,278)(125,273)(126,276)(127,275)
(128,274)(129,269)(130,272)(131,271)(132,270)(133,265)(134,268)(135,267)
(136,266)(137,261)(138,264)(139,263)(140,262)(141,313)(142,316)(143,315)
(144,314)(145,309)(146,312)(147,311)(148,310)(149,333)(150,336)(151,335)
(152,334)(153,329)(154,332)(155,331)(156,330)(157,325)(158,328)(159,327)
(160,326)(161,321)(162,324)(163,323)(164,322)(165,317)(166,320)(167,319)
(168,318)(337,537)(338,540)(339,539)(340,538)(341,533)(342,536)(343,535)
(344,534)(345,557)(346,560)(347,559)(348,558)(349,553)(350,556)(351,555)
(352,554)(353,549)(354,552)(355,551)(356,550)(357,545)(358,548)(359,547)
(360,546)(361,541)(362,544)(363,543)(364,542)(365,509)(366,512)(367,511)
(368,510)(369,505)(370,508)(371,507)(372,506)(373,529)(374,532)(375,531)
(376,530)(377,525)(378,528)(379,527)(380,526)(381,521)(382,524)(383,523)
(384,522)(385,517)(386,520)(387,519)(388,518)(389,513)(390,516)(391,515)
(392,514)(393,565)(394,568)(395,567)(396,566)(397,561)(398,564)(399,563)
(400,562)(401,585)(402,588)(403,587)(404,586)(405,581)(406,584)(407,583)
(408,582)(409,577)(410,580)(411,579)(412,578)(413,573)(414,576)(415,575)
(416,574)(417,569)(418,572)(419,571)(420,570)(421,621)(422,624)(423,623)
(424,622)(425,617)(426,620)(427,619)(428,618)(429,641)(430,644)(431,643)
(432,642)(433,637)(434,640)(435,639)(436,638)(437,633)(438,636)(439,635)
(440,634)(441,629)(442,632)(443,631)(444,630)(445,625)(446,628)(447,627)
(448,626)(449,593)(450,596)(451,595)(452,594)(453,589)(454,592)(455,591)
(456,590)(457,613)(458,616)(459,615)(460,614)(461,609)(462,612)(463,611)
(464,610)(465,605)(466,608)(467,607)(468,606)(469,601)(470,604)(471,603)
(472,602)(473,597)(474,600)(475,599)(476,598)(477,649)(478,652)(479,651)
(480,650)(481,645)(482,648)(483,647)(484,646)(485,669)(486,672)(487,671)
(488,670)(489,665)(490,668)(491,667)(492,666)(493,661)(494,664)(495,663)
(496,662)(497,657)(498,660)(499,659)(500,658)(501,653)(502,656)(503,655)
(504,654);
poly := sub<Sym(672)|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*s2*s1*s0*s1*s2*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 >;
References : None.
to this polytope