Polytope of Type {12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*1728h
if this polytope has a name.
Group : SmallGroup(1728,31623)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 108, 432, 72
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
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 : {12,4}*864d
3-fold quotients : {12,8}*576b
4-fold quotients : {6,4}*432b
6-fold quotients : {12,4}*288
9-fold quotients : {12,8}*192b
12-fold quotients : {6,4}*144
18-fold quotients : {12,4}*96a
24-fold quotients : {6,4}*72
27-fold quotients : {4,8}*64b
36-fold quotients : {12,2}*48, {6,4}*48a
54-fold quotients : {4,4}*32
72-fold quotients : {6,2}*24
108-fold quotients : {2,4}*16, {4,2}*16
144-fold quotients : {3,2}*12
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)( 8,330)
( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)( 16,346)
( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)( 24,341)
( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)
( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)( 40,376)
( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)( 48,362)
( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,379)( 56,381)
( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)( 64,397)
( 65,399)( 66,398)( 67,403)( 68,405)( 69,404)( 70,400)( 71,402)( 72,401)
( 73,388)( 74,390)( 75,389)( 76,394)( 77,396)( 78,395)( 79,391)( 80,393)
( 81,392)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)
( 89,411)( 90,410)( 91,424)( 92,426)( 93,425)( 94,430)( 95,432)( 96,431)
( 97,427)( 98,429)( 99,428)(100,415)(101,417)(102,416)(103,421)(104,423)
(105,422)(106,418)(107,420)(108,419)(109,217)(110,219)(111,218)(112,223)
(113,225)(114,224)(115,220)(116,222)(117,221)(118,235)(119,237)(120,236)
(121,241)(122,243)(123,242)(124,238)(125,240)(126,239)(127,226)(128,228)
(129,227)(130,232)(131,234)(132,233)(133,229)(134,231)(135,230)(136,244)
(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)(144,248)
(145,262)(146,264)(147,263)(148,268)(149,270)(150,269)(151,265)(152,267)
(153,266)(154,253)(155,255)(156,254)(157,259)(158,261)(159,260)(160,256)
(161,258)(162,257)(163,271)(164,273)(165,272)(166,277)(167,279)(168,278)
(169,274)(170,276)(171,275)(172,289)(173,291)(174,290)(175,295)(176,297)
(177,296)(178,292)(179,294)(180,293)(181,280)(182,282)(183,281)(184,286)
(185,288)(186,287)(187,283)(188,285)(189,284)(190,298)(191,300)(192,299)
(193,304)(194,306)(195,305)(196,301)(197,303)(198,302)(199,316)(200,318)
(201,317)(202,322)(203,324)(204,323)(205,319)(206,321)(207,320)(208,307)
(209,309)(210,308)(211,313)(212,315)(213,314)(214,310)(215,312)(216,311)
(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)
(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)(448,778)
(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)(456,773)
(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)(464,792)
(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)(472,808)
(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)(480,794)
(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,811)(488,813)
(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)(496,829)
(497,831)(498,830)(499,835)(500,837)(501,836)(502,832)(503,834)(504,833)
(505,820)(506,822)(507,821)(508,826)(509,828)(510,827)(511,823)(512,825)
(513,824)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)(520,841)
(521,843)(522,842)(523,856)(524,858)(525,857)(526,862)(527,864)(528,863)
(529,859)(530,861)(531,860)(532,847)(533,849)(534,848)(535,853)(536,855)
(537,854)(538,850)(539,852)(540,851)(541,649)(542,651)(543,650)(544,655)
(545,657)(546,656)(547,652)(548,654)(549,653)(550,667)(551,669)(552,668)
(553,673)(554,675)(555,674)(556,670)(557,672)(558,671)(559,658)(560,660)
(561,659)(562,664)(563,666)(564,665)(565,661)(566,663)(567,662)(568,676)
(569,678)(570,677)(571,682)(572,684)(573,683)(574,679)(575,681)(576,680)
(577,694)(578,696)(579,695)(580,700)(581,702)(582,701)(583,697)(584,699)
(585,698)(586,685)(587,687)(588,686)(589,691)(590,693)(591,692)(592,688)
(593,690)(594,689)(595,703)(596,705)(597,704)(598,709)(599,711)(600,710)
(601,706)(602,708)(603,707)(604,721)(605,723)(606,722)(607,727)(608,729)
(609,728)(610,724)(611,726)(612,725)(613,712)(614,714)(615,713)(616,718)
(617,720)(618,719)(619,715)(620,717)(621,716)(622,730)(623,732)(624,731)
(625,736)(626,738)(627,737)(628,733)(629,735)(630,734)(631,748)(632,750)
(633,749)(634,754)(635,756)(636,755)(637,751)(638,753)(639,752)(640,739)
(641,741)(642,740)(643,745)(644,747)(645,746)(646,742)(647,744)(648,743);;
s1 := ( 1,767)( 2,766)( 3,768)( 4,771)( 5,770)( 6,769)( 7,772)( 8,774)
( 9,773)( 10,758)( 11,757)( 12,759)( 13,762)( 14,761)( 15,760)( 16,763)
( 17,765)( 18,764)( 19,776)( 20,775)( 21,777)( 22,780)( 23,779)( 24,778)
( 25,781)( 26,783)( 27,782)( 28,794)( 29,793)( 30,795)( 31,798)( 32,797)
( 33,796)( 34,799)( 35,801)( 36,800)( 37,785)( 38,784)( 39,786)( 40,789)
( 41,788)( 42,787)( 43,790)( 44,792)( 45,791)( 46,803)( 47,802)( 48,804)
( 49,807)( 50,806)( 51,805)( 52,808)( 53,810)( 54,809)( 55,821)( 56,820)
( 57,822)( 58,825)( 59,824)( 60,823)( 61,826)( 62,828)( 63,827)( 64,812)
( 65,811)( 66,813)( 67,816)( 68,815)( 69,814)( 70,817)( 71,819)( 72,818)
( 73,830)( 74,829)( 75,831)( 76,834)( 77,833)( 78,832)( 79,835)( 80,837)
( 81,836)( 82,848)( 83,847)( 84,849)( 85,852)( 86,851)( 87,850)( 88,853)
( 89,855)( 90,854)( 91,839)( 92,838)( 93,840)( 94,843)( 95,842)( 96,841)
( 97,844)( 98,846)( 99,845)(100,857)(101,856)(102,858)(103,861)(104,860)
(105,859)(106,862)(107,864)(108,863)(109,659)(110,658)(111,660)(112,663)
(113,662)(114,661)(115,664)(116,666)(117,665)(118,650)(119,649)(120,651)
(121,654)(122,653)(123,652)(124,655)(125,657)(126,656)(127,668)(128,667)
(129,669)(130,672)(131,671)(132,670)(133,673)(134,675)(135,674)(136,686)
(137,685)(138,687)(139,690)(140,689)(141,688)(142,691)(143,693)(144,692)
(145,677)(146,676)(147,678)(148,681)(149,680)(150,679)(151,682)(152,684)
(153,683)(154,695)(155,694)(156,696)(157,699)(158,698)(159,697)(160,700)
(161,702)(162,701)(163,713)(164,712)(165,714)(166,717)(167,716)(168,715)
(169,718)(170,720)(171,719)(172,704)(173,703)(174,705)(175,708)(176,707)
(177,706)(178,709)(179,711)(180,710)(181,722)(182,721)(183,723)(184,726)
(185,725)(186,724)(187,727)(188,729)(189,728)(190,740)(191,739)(192,741)
(193,744)(194,743)(195,742)(196,745)(197,747)(198,746)(199,731)(200,730)
(201,732)(202,735)(203,734)(204,733)(205,736)(206,738)(207,737)(208,749)
(209,748)(210,750)(211,753)(212,752)(213,751)(214,754)(215,756)(216,755)
(217,605)(218,604)(219,606)(220,609)(221,608)(222,607)(223,610)(224,612)
(225,611)(226,596)(227,595)(228,597)(229,600)(230,599)(231,598)(232,601)
(233,603)(234,602)(235,614)(236,613)(237,615)(238,618)(239,617)(240,616)
(241,619)(242,621)(243,620)(244,632)(245,631)(246,633)(247,636)(248,635)
(249,634)(250,637)(251,639)(252,638)(253,623)(254,622)(255,624)(256,627)
(257,626)(258,625)(259,628)(260,630)(261,629)(262,641)(263,640)(264,642)
(265,645)(266,644)(267,643)(268,646)(269,648)(270,647)(271,551)(272,550)
(273,552)(274,555)(275,554)(276,553)(277,556)(278,558)(279,557)(280,542)
(281,541)(282,543)(283,546)(284,545)(285,544)(286,547)(287,549)(288,548)
(289,560)(290,559)(291,561)(292,564)(293,563)(294,562)(295,565)(296,567)
(297,566)(298,578)(299,577)(300,579)(301,582)(302,581)(303,580)(304,583)
(305,585)(306,584)(307,569)(308,568)(309,570)(310,573)(311,572)(312,571)
(313,574)(314,576)(315,575)(316,587)(317,586)(318,588)(319,591)(320,590)
(321,589)(322,592)(323,594)(324,593)(325,497)(326,496)(327,498)(328,501)
(329,500)(330,499)(331,502)(332,504)(333,503)(334,488)(335,487)(336,489)
(337,492)(338,491)(339,490)(340,493)(341,495)(342,494)(343,506)(344,505)
(345,507)(346,510)(347,509)(348,508)(349,511)(350,513)(351,512)(352,524)
(353,523)(354,525)(355,528)(356,527)(357,526)(358,529)(359,531)(360,530)
(361,515)(362,514)(363,516)(364,519)(365,518)(366,517)(367,520)(368,522)
(369,521)(370,533)(371,532)(372,534)(373,537)(374,536)(375,535)(376,538)
(377,540)(378,539)(379,443)(380,442)(381,444)(382,447)(383,446)(384,445)
(385,448)(386,450)(387,449)(388,434)(389,433)(390,435)(391,438)(392,437)
(393,436)(394,439)(395,441)(396,440)(397,452)(398,451)(399,453)(400,456)
(401,455)(402,454)(403,457)(404,459)(405,458)(406,470)(407,469)(408,471)
(409,474)(410,473)(411,472)(412,475)(413,477)(414,476)(415,461)(416,460)
(417,462)(418,465)(419,464)(420,463)(421,466)(422,468)(423,467)(424,479)
(425,478)(426,480)(427,483)(428,482)(429,481)(430,484)(431,486)(432,485);;
s2 := ( 1,109)( 2,114)( 3,116)( 4,112)( 5,117)( 6,110)( 7,115)( 8,111)
( 9,113)( 10,118)( 11,123)( 12,125)( 13,121)( 14,126)( 15,119)( 16,124)
( 17,120)( 18,122)( 19,127)( 20,132)( 21,134)( 22,130)( 23,135)( 24,128)
( 25,133)( 26,129)( 27,131)( 28,136)( 29,141)( 30,143)( 31,139)( 32,144)
( 33,137)( 34,142)( 35,138)( 36,140)( 37,145)( 38,150)( 39,152)( 40,148)
( 41,153)( 42,146)( 43,151)( 44,147)( 45,149)( 46,154)( 47,159)( 48,161)
( 49,157)( 50,162)( 51,155)( 52,160)( 53,156)( 54,158)( 55,190)( 56,195)
( 57,197)( 58,193)( 59,198)( 60,191)( 61,196)( 62,192)( 63,194)( 64,199)
( 65,204)( 66,206)( 67,202)( 68,207)( 69,200)( 70,205)( 71,201)( 72,203)
( 73,208)( 74,213)( 75,215)( 76,211)( 77,216)( 78,209)( 79,214)( 80,210)
( 81,212)( 82,163)( 83,168)( 84,170)( 85,166)( 86,171)( 87,164)( 88,169)
( 89,165)( 90,167)( 91,172)( 92,177)( 93,179)( 94,175)( 95,180)( 96,173)
( 97,178)( 98,174)( 99,176)(100,181)(101,186)(102,188)(103,184)(104,189)
(105,182)(106,187)(107,183)(108,185)(217,325)(218,330)(219,332)(220,328)
(221,333)(222,326)(223,331)(224,327)(225,329)(226,334)(227,339)(228,341)
(229,337)(230,342)(231,335)(232,340)(233,336)(234,338)(235,343)(236,348)
(237,350)(238,346)(239,351)(240,344)(241,349)(242,345)(243,347)(244,352)
(245,357)(246,359)(247,355)(248,360)(249,353)(250,358)(251,354)(252,356)
(253,361)(254,366)(255,368)(256,364)(257,369)(258,362)(259,367)(260,363)
(261,365)(262,370)(263,375)(264,377)(265,373)(266,378)(267,371)(268,376)
(269,372)(270,374)(271,406)(272,411)(273,413)(274,409)(275,414)(276,407)
(277,412)(278,408)(279,410)(280,415)(281,420)(282,422)(283,418)(284,423)
(285,416)(286,421)(287,417)(288,419)(289,424)(290,429)(291,431)(292,427)
(293,432)(294,425)(295,430)(296,426)(297,428)(298,379)(299,384)(300,386)
(301,382)(302,387)(303,380)(304,385)(305,381)(306,383)(307,388)(308,393)
(309,395)(310,391)(311,396)(312,389)(313,394)(314,390)(315,392)(316,397)
(317,402)(318,404)(319,400)(320,405)(321,398)(322,403)(323,399)(324,401)
(433,460)(434,465)(435,467)(436,463)(437,468)(438,461)(439,466)(440,462)
(441,464)(442,469)(443,474)(444,476)(445,472)(446,477)(447,470)(448,475)
(449,471)(450,473)(451,478)(452,483)(453,485)(454,481)(455,486)(456,479)
(457,484)(458,480)(459,482)(488,492)(489,494)(491,495)(497,501)(498,503)
(500,504)(506,510)(507,512)(509,513)(515,519)(516,521)(518,522)(524,528)
(525,530)(527,531)(533,537)(534,539)(536,540)(542,546)(543,548)(545,549)
(551,555)(552,557)(554,558)(560,564)(561,566)(563,567)(569,573)(570,575)
(572,576)(578,582)(579,584)(581,585)(587,591)(588,593)(590,594)(595,622)
(596,627)(597,629)(598,625)(599,630)(600,623)(601,628)(602,624)(603,626)
(604,631)(605,636)(606,638)(607,634)(608,639)(609,632)(610,637)(611,633)
(612,635)(613,640)(614,645)(615,647)(616,643)(617,648)(618,641)(619,646)
(620,642)(621,644)(650,654)(651,656)(653,657)(659,663)(660,665)(662,666)
(668,672)(669,674)(671,675)(677,681)(678,683)(680,684)(686,690)(687,692)
(689,693)(695,699)(696,701)(698,702)(703,730)(704,735)(705,737)(706,733)
(707,738)(708,731)(709,736)(710,732)(711,734)(712,739)(713,744)(714,746)
(715,742)(716,747)(717,740)(718,745)(719,741)(720,743)(721,748)(722,753)
(723,755)(724,751)(725,756)(726,749)(727,754)(728,750)(729,752)(757,784)
(758,789)(759,791)(760,787)(761,792)(762,785)(763,790)(764,786)(765,788)
(766,793)(767,798)(768,800)(769,796)(770,801)(771,794)(772,799)(773,795)
(774,797)(775,802)(776,807)(777,809)(778,805)(779,810)(780,803)(781,808)
(782,804)(783,806)(812,816)(813,818)(815,819)(821,825)(822,827)(824,828)
(830,834)(831,836)(833,837)(839,843)(840,845)(842,846)(848,852)(849,854)
(851,855)(857,861)(858,863)(860,864);;
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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*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,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) :
s0 := Sym(864)!( 1,325)( 2,327)( 3,326)( 4,331)( 5,333)( 6,332)( 7,328)
( 8,330)( 9,329)( 10,343)( 11,345)( 12,344)( 13,349)( 14,351)( 15,350)
( 16,346)( 17,348)( 18,347)( 19,334)( 20,336)( 21,335)( 22,340)( 23,342)
( 24,341)( 25,337)( 26,339)( 27,338)( 28,352)( 29,354)( 30,353)( 31,358)
( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,370)( 38,372)( 39,371)
( 40,376)( 41,378)( 42,377)( 43,373)( 44,375)( 45,374)( 46,361)( 47,363)
( 48,362)( 49,367)( 50,369)( 51,368)( 52,364)( 53,366)( 54,365)( 55,379)
( 56,381)( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)
( 64,397)( 65,399)( 66,398)( 67,403)( 68,405)( 69,404)( 70,400)( 71,402)
( 72,401)( 73,388)( 74,390)( 75,389)( 76,394)( 77,396)( 78,395)( 79,391)
( 80,393)( 81,392)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)
( 88,409)( 89,411)( 90,410)( 91,424)( 92,426)( 93,425)( 94,430)( 95,432)
( 96,431)( 97,427)( 98,429)( 99,428)(100,415)(101,417)(102,416)(103,421)
(104,423)(105,422)(106,418)(107,420)(108,419)(109,217)(110,219)(111,218)
(112,223)(113,225)(114,224)(115,220)(116,222)(117,221)(118,235)(119,237)
(120,236)(121,241)(122,243)(123,242)(124,238)(125,240)(126,239)(127,226)
(128,228)(129,227)(130,232)(131,234)(132,233)(133,229)(134,231)(135,230)
(136,244)(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)
(144,248)(145,262)(146,264)(147,263)(148,268)(149,270)(150,269)(151,265)
(152,267)(153,266)(154,253)(155,255)(156,254)(157,259)(158,261)(159,260)
(160,256)(161,258)(162,257)(163,271)(164,273)(165,272)(166,277)(167,279)
(168,278)(169,274)(170,276)(171,275)(172,289)(173,291)(174,290)(175,295)
(176,297)(177,296)(178,292)(179,294)(180,293)(181,280)(182,282)(183,281)
(184,286)(185,288)(186,287)(187,283)(188,285)(189,284)(190,298)(191,300)
(192,299)(193,304)(194,306)(195,305)(196,301)(197,303)(198,302)(199,316)
(200,318)(201,317)(202,322)(203,324)(204,323)(205,319)(206,321)(207,320)
(208,307)(209,309)(210,308)(211,313)(212,315)(213,314)(214,310)(215,312)
(216,311)(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)
(440,762)(441,761)(442,775)(443,777)(444,776)(445,781)(446,783)(447,782)
(448,778)(449,780)(450,779)(451,766)(452,768)(453,767)(454,772)(455,774)
(456,773)(457,769)(458,771)(459,770)(460,784)(461,786)(462,785)(463,790)
(464,792)(465,791)(466,787)(467,789)(468,788)(469,802)(470,804)(471,803)
(472,808)(473,810)(474,809)(475,805)(476,807)(477,806)(478,793)(479,795)
(480,794)(481,799)(482,801)(483,800)(484,796)(485,798)(486,797)(487,811)
(488,813)(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)
(496,829)(497,831)(498,830)(499,835)(500,837)(501,836)(502,832)(503,834)
(504,833)(505,820)(506,822)(507,821)(508,826)(509,828)(510,827)(511,823)
(512,825)(513,824)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)
(520,841)(521,843)(522,842)(523,856)(524,858)(525,857)(526,862)(527,864)
(528,863)(529,859)(530,861)(531,860)(532,847)(533,849)(534,848)(535,853)
(536,855)(537,854)(538,850)(539,852)(540,851)(541,649)(542,651)(543,650)
(544,655)(545,657)(546,656)(547,652)(548,654)(549,653)(550,667)(551,669)
(552,668)(553,673)(554,675)(555,674)(556,670)(557,672)(558,671)(559,658)
(560,660)(561,659)(562,664)(563,666)(564,665)(565,661)(566,663)(567,662)
(568,676)(569,678)(570,677)(571,682)(572,684)(573,683)(574,679)(575,681)
(576,680)(577,694)(578,696)(579,695)(580,700)(581,702)(582,701)(583,697)
(584,699)(585,698)(586,685)(587,687)(588,686)(589,691)(590,693)(591,692)
(592,688)(593,690)(594,689)(595,703)(596,705)(597,704)(598,709)(599,711)
(600,710)(601,706)(602,708)(603,707)(604,721)(605,723)(606,722)(607,727)
(608,729)(609,728)(610,724)(611,726)(612,725)(613,712)(614,714)(615,713)
(616,718)(617,720)(618,719)(619,715)(620,717)(621,716)(622,730)(623,732)
(624,731)(625,736)(626,738)(627,737)(628,733)(629,735)(630,734)(631,748)
(632,750)(633,749)(634,754)(635,756)(636,755)(637,751)(638,753)(639,752)
(640,739)(641,741)(642,740)(643,745)(644,747)(645,746)(646,742)(647,744)
(648,743);
s1 := Sym(864)!( 1,767)( 2,766)( 3,768)( 4,771)( 5,770)( 6,769)( 7,772)
( 8,774)( 9,773)( 10,758)( 11,757)( 12,759)( 13,762)( 14,761)( 15,760)
( 16,763)( 17,765)( 18,764)( 19,776)( 20,775)( 21,777)( 22,780)( 23,779)
( 24,778)( 25,781)( 26,783)( 27,782)( 28,794)( 29,793)( 30,795)( 31,798)
( 32,797)( 33,796)( 34,799)( 35,801)( 36,800)( 37,785)( 38,784)( 39,786)
( 40,789)( 41,788)( 42,787)( 43,790)( 44,792)( 45,791)( 46,803)( 47,802)
( 48,804)( 49,807)( 50,806)( 51,805)( 52,808)( 53,810)( 54,809)( 55,821)
( 56,820)( 57,822)( 58,825)( 59,824)( 60,823)( 61,826)( 62,828)( 63,827)
( 64,812)( 65,811)( 66,813)( 67,816)( 68,815)( 69,814)( 70,817)( 71,819)
( 72,818)( 73,830)( 74,829)( 75,831)( 76,834)( 77,833)( 78,832)( 79,835)
( 80,837)( 81,836)( 82,848)( 83,847)( 84,849)( 85,852)( 86,851)( 87,850)
( 88,853)( 89,855)( 90,854)( 91,839)( 92,838)( 93,840)( 94,843)( 95,842)
( 96,841)( 97,844)( 98,846)( 99,845)(100,857)(101,856)(102,858)(103,861)
(104,860)(105,859)(106,862)(107,864)(108,863)(109,659)(110,658)(111,660)
(112,663)(113,662)(114,661)(115,664)(116,666)(117,665)(118,650)(119,649)
(120,651)(121,654)(122,653)(123,652)(124,655)(125,657)(126,656)(127,668)
(128,667)(129,669)(130,672)(131,671)(132,670)(133,673)(134,675)(135,674)
(136,686)(137,685)(138,687)(139,690)(140,689)(141,688)(142,691)(143,693)
(144,692)(145,677)(146,676)(147,678)(148,681)(149,680)(150,679)(151,682)
(152,684)(153,683)(154,695)(155,694)(156,696)(157,699)(158,698)(159,697)
(160,700)(161,702)(162,701)(163,713)(164,712)(165,714)(166,717)(167,716)
(168,715)(169,718)(170,720)(171,719)(172,704)(173,703)(174,705)(175,708)
(176,707)(177,706)(178,709)(179,711)(180,710)(181,722)(182,721)(183,723)
(184,726)(185,725)(186,724)(187,727)(188,729)(189,728)(190,740)(191,739)
(192,741)(193,744)(194,743)(195,742)(196,745)(197,747)(198,746)(199,731)
(200,730)(201,732)(202,735)(203,734)(204,733)(205,736)(206,738)(207,737)
(208,749)(209,748)(210,750)(211,753)(212,752)(213,751)(214,754)(215,756)
(216,755)(217,605)(218,604)(219,606)(220,609)(221,608)(222,607)(223,610)
(224,612)(225,611)(226,596)(227,595)(228,597)(229,600)(230,599)(231,598)
(232,601)(233,603)(234,602)(235,614)(236,613)(237,615)(238,618)(239,617)
(240,616)(241,619)(242,621)(243,620)(244,632)(245,631)(246,633)(247,636)
(248,635)(249,634)(250,637)(251,639)(252,638)(253,623)(254,622)(255,624)
(256,627)(257,626)(258,625)(259,628)(260,630)(261,629)(262,641)(263,640)
(264,642)(265,645)(266,644)(267,643)(268,646)(269,648)(270,647)(271,551)
(272,550)(273,552)(274,555)(275,554)(276,553)(277,556)(278,558)(279,557)
(280,542)(281,541)(282,543)(283,546)(284,545)(285,544)(286,547)(287,549)
(288,548)(289,560)(290,559)(291,561)(292,564)(293,563)(294,562)(295,565)
(296,567)(297,566)(298,578)(299,577)(300,579)(301,582)(302,581)(303,580)
(304,583)(305,585)(306,584)(307,569)(308,568)(309,570)(310,573)(311,572)
(312,571)(313,574)(314,576)(315,575)(316,587)(317,586)(318,588)(319,591)
(320,590)(321,589)(322,592)(323,594)(324,593)(325,497)(326,496)(327,498)
(328,501)(329,500)(330,499)(331,502)(332,504)(333,503)(334,488)(335,487)
(336,489)(337,492)(338,491)(339,490)(340,493)(341,495)(342,494)(343,506)
(344,505)(345,507)(346,510)(347,509)(348,508)(349,511)(350,513)(351,512)
(352,524)(353,523)(354,525)(355,528)(356,527)(357,526)(358,529)(359,531)
(360,530)(361,515)(362,514)(363,516)(364,519)(365,518)(366,517)(367,520)
(368,522)(369,521)(370,533)(371,532)(372,534)(373,537)(374,536)(375,535)
(376,538)(377,540)(378,539)(379,443)(380,442)(381,444)(382,447)(383,446)
(384,445)(385,448)(386,450)(387,449)(388,434)(389,433)(390,435)(391,438)
(392,437)(393,436)(394,439)(395,441)(396,440)(397,452)(398,451)(399,453)
(400,456)(401,455)(402,454)(403,457)(404,459)(405,458)(406,470)(407,469)
(408,471)(409,474)(410,473)(411,472)(412,475)(413,477)(414,476)(415,461)
(416,460)(417,462)(418,465)(419,464)(420,463)(421,466)(422,468)(423,467)
(424,479)(425,478)(426,480)(427,483)(428,482)(429,481)(430,484)(431,486)
(432,485);
s2 := Sym(864)!( 1,109)( 2,114)( 3,116)( 4,112)( 5,117)( 6,110)( 7,115)
( 8,111)( 9,113)( 10,118)( 11,123)( 12,125)( 13,121)( 14,126)( 15,119)
( 16,124)( 17,120)( 18,122)( 19,127)( 20,132)( 21,134)( 22,130)( 23,135)
( 24,128)( 25,133)( 26,129)( 27,131)( 28,136)( 29,141)( 30,143)( 31,139)
( 32,144)( 33,137)( 34,142)( 35,138)( 36,140)( 37,145)( 38,150)( 39,152)
( 40,148)( 41,153)( 42,146)( 43,151)( 44,147)( 45,149)( 46,154)( 47,159)
( 48,161)( 49,157)( 50,162)( 51,155)( 52,160)( 53,156)( 54,158)( 55,190)
( 56,195)( 57,197)( 58,193)( 59,198)( 60,191)( 61,196)( 62,192)( 63,194)
( 64,199)( 65,204)( 66,206)( 67,202)( 68,207)( 69,200)( 70,205)( 71,201)
( 72,203)( 73,208)( 74,213)( 75,215)( 76,211)( 77,216)( 78,209)( 79,214)
( 80,210)( 81,212)( 82,163)( 83,168)( 84,170)( 85,166)( 86,171)( 87,164)
( 88,169)( 89,165)( 90,167)( 91,172)( 92,177)( 93,179)( 94,175)( 95,180)
( 96,173)( 97,178)( 98,174)( 99,176)(100,181)(101,186)(102,188)(103,184)
(104,189)(105,182)(106,187)(107,183)(108,185)(217,325)(218,330)(219,332)
(220,328)(221,333)(222,326)(223,331)(224,327)(225,329)(226,334)(227,339)
(228,341)(229,337)(230,342)(231,335)(232,340)(233,336)(234,338)(235,343)
(236,348)(237,350)(238,346)(239,351)(240,344)(241,349)(242,345)(243,347)
(244,352)(245,357)(246,359)(247,355)(248,360)(249,353)(250,358)(251,354)
(252,356)(253,361)(254,366)(255,368)(256,364)(257,369)(258,362)(259,367)
(260,363)(261,365)(262,370)(263,375)(264,377)(265,373)(266,378)(267,371)
(268,376)(269,372)(270,374)(271,406)(272,411)(273,413)(274,409)(275,414)
(276,407)(277,412)(278,408)(279,410)(280,415)(281,420)(282,422)(283,418)
(284,423)(285,416)(286,421)(287,417)(288,419)(289,424)(290,429)(291,431)
(292,427)(293,432)(294,425)(295,430)(296,426)(297,428)(298,379)(299,384)
(300,386)(301,382)(302,387)(303,380)(304,385)(305,381)(306,383)(307,388)
(308,393)(309,395)(310,391)(311,396)(312,389)(313,394)(314,390)(315,392)
(316,397)(317,402)(318,404)(319,400)(320,405)(321,398)(322,403)(323,399)
(324,401)(433,460)(434,465)(435,467)(436,463)(437,468)(438,461)(439,466)
(440,462)(441,464)(442,469)(443,474)(444,476)(445,472)(446,477)(447,470)
(448,475)(449,471)(450,473)(451,478)(452,483)(453,485)(454,481)(455,486)
(456,479)(457,484)(458,480)(459,482)(488,492)(489,494)(491,495)(497,501)
(498,503)(500,504)(506,510)(507,512)(509,513)(515,519)(516,521)(518,522)
(524,528)(525,530)(527,531)(533,537)(534,539)(536,540)(542,546)(543,548)
(545,549)(551,555)(552,557)(554,558)(560,564)(561,566)(563,567)(569,573)
(570,575)(572,576)(578,582)(579,584)(581,585)(587,591)(588,593)(590,594)
(595,622)(596,627)(597,629)(598,625)(599,630)(600,623)(601,628)(602,624)
(603,626)(604,631)(605,636)(606,638)(607,634)(608,639)(609,632)(610,637)
(611,633)(612,635)(613,640)(614,645)(615,647)(616,643)(617,648)(618,641)
(619,646)(620,642)(621,644)(650,654)(651,656)(653,657)(659,663)(660,665)
(662,666)(668,672)(669,674)(671,675)(677,681)(678,683)(680,684)(686,690)
(687,692)(689,693)(695,699)(696,701)(698,702)(703,730)(704,735)(705,737)
(706,733)(707,738)(708,731)(709,736)(710,732)(711,734)(712,739)(713,744)
(714,746)(715,742)(716,747)(717,740)(718,745)(719,741)(720,743)(721,748)
(722,753)(723,755)(724,751)(725,756)(726,749)(727,754)(728,750)(729,752)
(757,784)(758,789)(759,791)(760,787)(761,792)(762,785)(763,790)(764,786)
(765,788)(766,793)(767,798)(768,800)(769,796)(770,801)(771,794)(772,799)
(773,795)(774,797)(775,802)(776,807)(777,809)(778,805)(779,810)(780,803)
(781,808)(782,804)(783,806)(812,816)(813,818)(815,819)(821,825)(822,827)
(824,828)(830,834)(831,836)(833,837)(839,843)(840,845)(842,846)(848,852)
(849,854)(851,855)(857,861)(858,863)(860,864);
poly := sub<Sym(864)|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*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1,
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s2*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,
s2*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope