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Polytope of Type {84,4}

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