Polytope of Type {12,8}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,8}*1728a
if this polytope has a name.
Group : SmallGroup(1728,12653)
Rank : 3
Schlafli Type : {12,8}
Number of vertices, edges, etc : 108, 432, 72
Order of s0s1s2 : 24
Order of s0s1s2s1 : 6
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 : {6,8}*864a, {12,4}*864b
3-fold quotients : {12,8}*576a
4-fold quotients : {6,4}*432a
6-fold quotients : {6,8}*288, {12,4}*288
8-fold quotients : {6,4}*216
12-fold quotients : {6,4}*144
24-fold quotients : {6,4}*72
27-fold quotients : {4,8}*64a
54-fold quotients : {4,4}*32, {2,8}*32
108-fold quotients : {2,4}*16, {4,2}*16
216-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
s0 := ( 1,325)( 2,326)( 3,327)( 4,333)( 5,331)( 6,332)( 7,329)( 8,330)
( 9,328)( 10,345)( 11,343)( 12,344)( 13,350)( 14,351)( 15,349)( 16,346)
( 17,347)( 18,348)( 19,335)( 20,336)( 21,334)( 22,340)( 23,341)( 24,342)
( 25,339)( 26,337)( 27,338)( 28,352)( 29,353)( 30,354)( 31,360)( 32,358)
( 33,359)( 34,356)( 35,357)( 36,355)( 37,372)( 38,370)( 39,371)( 40,377)
( 41,378)( 42,376)( 43,373)( 44,374)( 45,375)( 46,362)( 47,363)( 48,361)
( 49,367)( 50,368)( 51,369)( 52,366)( 53,364)( 54,365)( 55,379)( 56,380)
( 57,381)( 58,387)( 59,385)( 60,386)( 61,383)( 62,384)( 63,382)( 64,399)
( 65,397)( 66,398)( 67,404)( 68,405)( 69,403)( 70,400)( 71,401)( 72,402)
( 73,389)( 74,390)( 75,388)( 76,394)( 77,395)( 78,396)( 79,393)( 80,391)
( 81,392)( 82,406)( 83,407)( 84,408)( 85,414)( 86,412)( 87,413)( 88,410)
( 89,411)( 90,409)( 91,426)( 92,424)( 93,425)( 94,431)( 95,432)( 96,430)
( 97,427)( 98,428)( 99,429)(100,416)(101,417)(102,415)(103,421)(104,422)
(105,423)(106,420)(107,418)(108,419)(109,244)(110,245)(111,246)(112,252)
(113,250)(114,251)(115,248)(116,249)(117,247)(118,264)(119,262)(120,263)
(121,269)(122,270)(123,268)(124,265)(125,266)(126,267)(127,254)(128,255)
(129,253)(130,259)(131,260)(132,261)(133,258)(134,256)(135,257)(136,217)
(137,218)(138,219)(139,225)(140,223)(141,224)(142,221)(143,222)(144,220)
(145,237)(146,235)(147,236)(148,242)(149,243)(150,241)(151,238)(152,239)
(153,240)(154,227)(155,228)(156,226)(157,232)(158,233)(159,234)(160,231)
(161,229)(162,230)(163,298)(164,299)(165,300)(166,306)(167,304)(168,305)
(169,302)(170,303)(171,301)(172,318)(173,316)(174,317)(175,323)(176,324)
(177,322)(178,319)(179,320)(180,321)(181,308)(182,309)(183,307)(184,313)
(185,314)(186,315)(187,312)(188,310)(189,311)(190,271)(191,272)(192,273)
(193,279)(194,277)(195,278)(196,275)(197,276)(198,274)(199,291)(200,289)
(201,290)(202,296)(203,297)(204,295)(205,292)(206,293)(207,294)(208,281)
(209,282)(210,280)(211,286)(212,287)(213,288)(214,285)(215,283)(216,284)
(433,757)(434,758)(435,759)(436,765)(437,763)(438,764)(439,761)(440,762)
(441,760)(442,777)(443,775)(444,776)(445,782)(446,783)(447,781)(448,778)
(449,779)(450,780)(451,767)(452,768)(453,766)(454,772)(455,773)(456,774)
(457,771)(458,769)(459,770)(460,784)(461,785)(462,786)(463,792)(464,790)
(465,791)(466,788)(467,789)(468,787)(469,804)(470,802)(471,803)(472,809)
(473,810)(474,808)(475,805)(476,806)(477,807)(478,794)(479,795)(480,793)
(481,799)(482,800)(483,801)(484,798)(485,796)(486,797)(487,811)(488,812)
(489,813)(490,819)(491,817)(492,818)(493,815)(494,816)(495,814)(496,831)
(497,829)(498,830)(499,836)(500,837)(501,835)(502,832)(503,833)(504,834)
(505,821)(506,822)(507,820)(508,826)(509,827)(510,828)(511,825)(512,823)
(513,824)(514,838)(515,839)(516,840)(517,846)(518,844)(519,845)(520,842)
(521,843)(522,841)(523,858)(524,856)(525,857)(526,863)(527,864)(528,862)
(529,859)(530,860)(531,861)(532,848)(533,849)(534,847)(535,853)(536,854)
(537,855)(538,852)(539,850)(540,851)(541,676)(542,677)(543,678)(544,684)
(545,682)(546,683)(547,680)(548,681)(549,679)(550,696)(551,694)(552,695)
(553,701)(554,702)(555,700)(556,697)(557,698)(558,699)(559,686)(560,687)
(561,685)(562,691)(563,692)(564,693)(565,690)(566,688)(567,689)(568,649)
(569,650)(570,651)(571,657)(572,655)(573,656)(574,653)(575,654)(576,652)
(577,669)(578,667)(579,668)(580,674)(581,675)(582,673)(583,670)(584,671)
(585,672)(586,659)(587,660)(588,658)(589,664)(590,665)(591,666)(592,663)
(593,661)(594,662)(595,730)(596,731)(597,732)(598,738)(599,736)(600,737)
(601,734)(602,735)(603,733)(604,750)(605,748)(606,749)(607,755)(608,756)
(609,754)(610,751)(611,752)(612,753)(613,740)(614,741)(615,739)(616,745)
(617,746)(618,747)(619,744)(620,742)(621,743)(622,703)(623,704)(624,705)
(625,711)(626,709)(627,710)(628,707)(629,708)(630,706)(631,723)(632,721)
(633,722)(634,728)(635,729)(636,727)(637,724)(638,725)(639,726)(640,713)
(641,714)(642,712)(643,718)(644,719)(645,720)(646,717)(647,715)(648,716);;
s1 := ( 1,544)( 2,546)( 3,545)( 4,541)( 5,543)( 6,542)( 7,547)( 8,549)
( 9,548)( 10,558)( 11,557)( 12,556)( 13,555)( 14,554)( 15,553)( 16,552)
( 17,551)( 18,550)( 19,561)( 20,560)( 21,559)( 22,567)( 23,566)( 24,565)
( 25,564)( 26,563)( 27,562)( 28,571)( 29,573)( 30,572)( 31,568)( 32,570)
( 33,569)( 34,574)( 35,576)( 36,575)( 37,585)( 38,584)( 39,583)( 40,582)
( 41,581)( 42,580)( 43,579)( 44,578)( 45,577)( 46,588)( 47,587)( 48,586)
( 49,594)( 50,593)( 51,592)( 52,591)( 53,590)( 54,589)( 55,598)( 56,600)
( 57,599)( 58,595)( 59,597)( 60,596)( 61,601)( 62,603)( 63,602)( 64,612)
( 65,611)( 66,610)( 67,609)( 68,608)( 69,607)( 70,606)( 71,605)( 72,604)
( 73,615)( 74,614)( 75,613)( 76,621)( 77,620)( 78,619)( 79,618)( 80,617)
( 81,616)( 82,625)( 83,627)( 84,626)( 85,622)( 86,624)( 87,623)( 88,628)
( 89,630)( 90,629)( 91,639)( 92,638)( 93,637)( 94,636)( 95,635)( 96,634)
( 97,633)( 98,632)( 99,631)(100,642)(101,641)(102,640)(103,648)(104,647)
(105,646)(106,645)(107,644)(108,643)(109,436)(110,438)(111,437)(112,433)
(113,435)(114,434)(115,439)(116,441)(117,440)(118,450)(119,449)(120,448)
(121,447)(122,446)(123,445)(124,444)(125,443)(126,442)(127,453)(128,452)
(129,451)(130,459)(131,458)(132,457)(133,456)(134,455)(135,454)(136,463)
(137,465)(138,464)(139,460)(140,462)(141,461)(142,466)(143,468)(144,467)
(145,477)(146,476)(147,475)(148,474)(149,473)(150,472)(151,471)(152,470)
(153,469)(154,480)(155,479)(156,478)(157,486)(158,485)(159,484)(160,483)
(161,482)(162,481)(163,490)(164,492)(165,491)(166,487)(167,489)(168,488)
(169,493)(170,495)(171,494)(172,504)(173,503)(174,502)(175,501)(176,500)
(177,499)(178,498)(179,497)(180,496)(181,507)(182,506)(183,505)(184,513)
(185,512)(186,511)(187,510)(188,509)(189,508)(190,517)(191,519)(192,518)
(193,514)(194,516)(195,515)(196,520)(197,522)(198,521)(199,531)(200,530)
(201,529)(202,528)(203,527)(204,526)(205,525)(206,524)(207,523)(208,534)
(209,533)(210,532)(211,540)(212,539)(213,538)(214,537)(215,536)(216,535)
(217,814)(218,816)(219,815)(220,811)(221,813)(222,812)(223,817)(224,819)
(225,818)(226,828)(227,827)(228,826)(229,825)(230,824)(231,823)(232,822)
(233,821)(234,820)(235,831)(236,830)(237,829)(238,837)(239,836)(240,835)
(241,834)(242,833)(243,832)(244,841)(245,843)(246,842)(247,838)(248,840)
(249,839)(250,844)(251,846)(252,845)(253,855)(254,854)(255,853)(256,852)
(257,851)(258,850)(259,849)(260,848)(261,847)(262,858)(263,857)(264,856)
(265,864)(266,863)(267,862)(268,861)(269,860)(270,859)(271,760)(272,762)
(273,761)(274,757)(275,759)(276,758)(277,763)(278,765)(279,764)(280,774)
(281,773)(282,772)(283,771)(284,770)(285,769)(286,768)(287,767)(288,766)
(289,777)(290,776)(291,775)(292,783)(293,782)(294,781)(295,780)(296,779)
(297,778)(298,787)(299,789)(300,788)(301,784)(302,786)(303,785)(304,790)
(305,792)(306,791)(307,801)(308,800)(309,799)(310,798)(311,797)(312,796)
(313,795)(314,794)(315,793)(316,804)(317,803)(318,802)(319,810)(320,809)
(321,808)(322,807)(323,806)(324,805)(325,706)(326,708)(327,707)(328,703)
(329,705)(330,704)(331,709)(332,711)(333,710)(334,720)(335,719)(336,718)
(337,717)(338,716)(339,715)(340,714)(341,713)(342,712)(343,723)(344,722)
(345,721)(346,729)(347,728)(348,727)(349,726)(350,725)(351,724)(352,733)
(353,735)(354,734)(355,730)(356,732)(357,731)(358,736)(359,738)(360,737)
(361,747)(362,746)(363,745)(364,744)(365,743)(366,742)(367,741)(368,740)
(369,739)(370,750)(371,749)(372,748)(373,756)(374,755)(375,754)(376,753)
(377,752)(378,751)(379,652)(380,654)(381,653)(382,649)(383,651)(384,650)
(385,655)(386,657)(387,656)(388,666)(389,665)(390,664)(391,663)(392,662)
(393,661)(394,660)(395,659)(396,658)(397,669)(398,668)(399,667)(400,675)
(401,674)(402,673)(403,672)(404,671)(405,670)(406,679)(407,681)(408,680)
(409,676)(410,678)(411,677)(412,682)(413,684)(414,683)(415,693)(416,692)
(417,691)(418,690)(419,689)(420,688)(421,687)(422,686)(423,685)(424,696)
(425,695)(426,694)(427,702)(428,701)(429,700)(430,699)(431,698)(432,697);;
s2 := ( 1,109)( 2,111)( 3,110)( 4,124)( 5,126)( 6,125)( 7,132)( 8,131)
( 9,130)( 10,119)( 11,118)( 12,120)( 13,134)( 14,133)( 15,135)( 16,112)
( 17,114)( 18,113)( 19,129)( 20,128)( 21,127)( 22,117)( 23,116)( 24,115)
( 25,122)( 26,121)( 27,123)( 28,136)( 29,138)( 30,137)( 31,151)( 32,153)
( 33,152)( 34,159)( 35,158)( 36,157)( 37,146)( 38,145)( 39,147)( 40,161)
( 41,160)( 42,162)( 43,139)( 44,141)( 45,140)( 46,156)( 47,155)( 48,154)
( 49,144)( 50,143)( 51,142)( 52,149)( 53,148)( 54,150)( 55,163)( 56,165)
( 57,164)( 58,178)( 59,180)( 60,179)( 61,186)( 62,185)( 63,184)( 64,173)
( 65,172)( 66,174)( 67,188)( 68,187)( 69,189)( 70,166)( 71,168)( 72,167)
( 73,183)( 74,182)( 75,181)( 76,171)( 77,170)( 78,169)( 79,176)( 80,175)
( 81,177)( 82,190)( 83,192)( 84,191)( 85,205)( 86,207)( 87,206)( 88,213)
( 89,212)( 90,211)( 91,200)( 92,199)( 93,201)( 94,215)( 95,214)( 96,216)
( 97,193)( 98,195)( 99,194)(100,210)(101,209)(102,208)(103,198)(104,197)
(105,196)(106,203)(107,202)(108,204)(217,352)(218,354)(219,353)(220,367)
(221,369)(222,368)(223,375)(224,374)(225,373)(226,362)(227,361)(228,363)
(229,377)(230,376)(231,378)(232,355)(233,357)(234,356)(235,372)(236,371)
(237,370)(238,360)(239,359)(240,358)(241,365)(242,364)(243,366)(244,325)
(245,327)(246,326)(247,340)(248,342)(249,341)(250,348)(251,347)(252,346)
(253,335)(254,334)(255,336)(256,350)(257,349)(258,351)(259,328)(260,330)
(261,329)(262,345)(263,344)(264,343)(265,333)(266,332)(267,331)(268,338)
(269,337)(270,339)(271,406)(272,408)(273,407)(274,421)(275,423)(276,422)
(277,429)(278,428)(279,427)(280,416)(281,415)(282,417)(283,431)(284,430)
(285,432)(286,409)(287,411)(288,410)(289,426)(290,425)(291,424)(292,414)
(293,413)(294,412)(295,419)(296,418)(297,420)(298,379)(299,381)(300,380)
(301,394)(302,396)(303,395)(304,402)(305,401)(306,400)(307,389)(308,388)
(309,390)(310,404)(311,403)(312,405)(313,382)(314,384)(315,383)(316,399)
(317,398)(318,397)(319,387)(320,386)(321,385)(322,392)(323,391)(324,393)
(433,460)(434,462)(435,461)(436,475)(437,477)(438,476)(439,483)(440,482)
(441,481)(442,470)(443,469)(444,471)(445,485)(446,484)(447,486)(448,463)
(449,465)(450,464)(451,480)(452,479)(453,478)(454,468)(455,467)(456,466)
(457,473)(458,472)(459,474)(487,514)(488,516)(489,515)(490,529)(491,531)
(492,530)(493,537)(494,536)(495,535)(496,524)(497,523)(498,525)(499,539)
(500,538)(501,540)(502,517)(503,519)(504,518)(505,534)(506,533)(507,532)
(508,522)(509,521)(510,520)(511,527)(512,526)(513,528)(542,543)(544,556)
(545,558)(546,557)(547,564)(548,563)(549,562)(550,551)(553,566)(554,565)
(555,567)(559,561)(569,570)(571,583)(572,585)(573,584)(574,591)(575,590)
(576,589)(577,578)(580,593)(581,592)(582,594)(586,588)(596,597)(598,610)
(599,612)(600,611)(601,618)(602,617)(603,616)(604,605)(607,620)(608,619)
(609,621)(613,615)(623,624)(625,637)(626,639)(627,638)(628,645)(629,644)
(630,643)(631,632)(634,647)(635,646)(636,648)(640,642)(650,651)(652,664)
(653,666)(654,665)(655,672)(656,671)(657,670)(658,659)(661,674)(662,673)
(663,675)(667,669)(677,678)(679,691)(680,693)(681,692)(682,699)(683,698)
(684,697)(685,686)(688,701)(689,700)(690,702)(694,696)(704,705)(706,718)
(707,720)(708,719)(709,726)(710,725)(711,724)(712,713)(715,728)(716,727)
(717,729)(721,723)(731,732)(733,745)(734,747)(735,746)(736,753)(737,752)
(738,751)(739,740)(742,755)(743,754)(744,756)(748,750)(757,784)(758,786)
(759,785)(760,799)(761,801)(762,800)(763,807)(764,806)(765,805)(766,794)
(767,793)(768,795)(769,809)(770,808)(771,810)(772,787)(773,789)(774,788)
(775,804)(776,803)(777,802)(778,792)(779,791)(780,790)(781,797)(782,796)
(783,798)(811,838)(812,840)(813,839)(814,853)(815,855)(816,854)(817,861)
(818,860)(819,859)(820,848)(821,847)(822,849)(823,863)(824,862)(825,864)
(826,841)(827,843)(828,842)(829,858)(830,857)(831,856)(832,846)(833,845)
(834,844)(835,851)(836,850)(837,852);;
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*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*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*s1*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)( 2,326)( 3,327)( 4,333)( 5,331)( 6,332)( 7,329)
( 8,330)( 9,328)( 10,345)( 11,343)( 12,344)( 13,350)( 14,351)( 15,349)
( 16,346)( 17,347)( 18,348)( 19,335)( 20,336)( 21,334)( 22,340)( 23,341)
( 24,342)( 25,339)( 26,337)( 27,338)( 28,352)( 29,353)( 30,354)( 31,360)
( 32,358)( 33,359)( 34,356)( 35,357)( 36,355)( 37,372)( 38,370)( 39,371)
( 40,377)( 41,378)( 42,376)( 43,373)( 44,374)( 45,375)( 46,362)( 47,363)
( 48,361)( 49,367)( 50,368)( 51,369)( 52,366)( 53,364)( 54,365)( 55,379)
( 56,380)( 57,381)( 58,387)( 59,385)( 60,386)( 61,383)( 62,384)( 63,382)
( 64,399)( 65,397)( 66,398)( 67,404)( 68,405)( 69,403)( 70,400)( 71,401)
( 72,402)( 73,389)( 74,390)( 75,388)( 76,394)( 77,395)( 78,396)( 79,393)
( 80,391)( 81,392)( 82,406)( 83,407)( 84,408)( 85,414)( 86,412)( 87,413)
( 88,410)( 89,411)( 90,409)( 91,426)( 92,424)( 93,425)( 94,431)( 95,432)
( 96,430)( 97,427)( 98,428)( 99,429)(100,416)(101,417)(102,415)(103,421)
(104,422)(105,423)(106,420)(107,418)(108,419)(109,244)(110,245)(111,246)
(112,252)(113,250)(114,251)(115,248)(116,249)(117,247)(118,264)(119,262)
(120,263)(121,269)(122,270)(123,268)(124,265)(125,266)(126,267)(127,254)
(128,255)(129,253)(130,259)(131,260)(132,261)(133,258)(134,256)(135,257)
(136,217)(137,218)(138,219)(139,225)(140,223)(141,224)(142,221)(143,222)
(144,220)(145,237)(146,235)(147,236)(148,242)(149,243)(150,241)(151,238)
(152,239)(153,240)(154,227)(155,228)(156,226)(157,232)(158,233)(159,234)
(160,231)(161,229)(162,230)(163,298)(164,299)(165,300)(166,306)(167,304)
(168,305)(169,302)(170,303)(171,301)(172,318)(173,316)(174,317)(175,323)
(176,324)(177,322)(178,319)(179,320)(180,321)(181,308)(182,309)(183,307)
(184,313)(185,314)(186,315)(187,312)(188,310)(189,311)(190,271)(191,272)
(192,273)(193,279)(194,277)(195,278)(196,275)(197,276)(198,274)(199,291)
(200,289)(201,290)(202,296)(203,297)(204,295)(205,292)(206,293)(207,294)
(208,281)(209,282)(210,280)(211,286)(212,287)(213,288)(214,285)(215,283)
(216,284)(433,757)(434,758)(435,759)(436,765)(437,763)(438,764)(439,761)
(440,762)(441,760)(442,777)(443,775)(444,776)(445,782)(446,783)(447,781)
(448,778)(449,779)(450,780)(451,767)(452,768)(453,766)(454,772)(455,773)
(456,774)(457,771)(458,769)(459,770)(460,784)(461,785)(462,786)(463,792)
(464,790)(465,791)(466,788)(467,789)(468,787)(469,804)(470,802)(471,803)
(472,809)(473,810)(474,808)(475,805)(476,806)(477,807)(478,794)(479,795)
(480,793)(481,799)(482,800)(483,801)(484,798)(485,796)(486,797)(487,811)
(488,812)(489,813)(490,819)(491,817)(492,818)(493,815)(494,816)(495,814)
(496,831)(497,829)(498,830)(499,836)(500,837)(501,835)(502,832)(503,833)
(504,834)(505,821)(506,822)(507,820)(508,826)(509,827)(510,828)(511,825)
(512,823)(513,824)(514,838)(515,839)(516,840)(517,846)(518,844)(519,845)
(520,842)(521,843)(522,841)(523,858)(524,856)(525,857)(526,863)(527,864)
(528,862)(529,859)(530,860)(531,861)(532,848)(533,849)(534,847)(535,853)
(536,854)(537,855)(538,852)(539,850)(540,851)(541,676)(542,677)(543,678)
(544,684)(545,682)(546,683)(547,680)(548,681)(549,679)(550,696)(551,694)
(552,695)(553,701)(554,702)(555,700)(556,697)(557,698)(558,699)(559,686)
(560,687)(561,685)(562,691)(563,692)(564,693)(565,690)(566,688)(567,689)
(568,649)(569,650)(570,651)(571,657)(572,655)(573,656)(574,653)(575,654)
(576,652)(577,669)(578,667)(579,668)(580,674)(581,675)(582,673)(583,670)
(584,671)(585,672)(586,659)(587,660)(588,658)(589,664)(590,665)(591,666)
(592,663)(593,661)(594,662)(595,730)(596,731)(597,732)(598,738)(599,736)
(600,737)(601,734)(602,735)(603,733)(604,750)(605,748)(606,749)(607,755)
(608,756)(609,754)(610,751)(611,752)(612,753)(613,740)(614,741)(615,739)
(616,745)(617,746)(618,747)(619,744)(620,742)(621,743)(622,703)(623,704)
(624,705)(625,711)(626,709)(627,710)(628,707)(629,708)(630,706)(631,723)
(632,721)(633,722)(634,728)(635,729)(636,727)(637,724)(638,725)(639,726)
(640,713)(641,714)(642,712)(643,718)(644,719)(645,720)(646,717)(647,715)
(648,716);
s1 := Sym(864)!( 1,544)( 2,546)( 3,545)( 4,541)( 5,543)( 6,542)( 7,547)
( 8,549)( 9,548)( 10,558)( 11,557)( 12,556)( 13,555)( 14,554)( 15,553)
( 16,552)( 17,551)( 18,550)( 19,561)( 20,560)( 21,559)( 22,567)( 23,566)
( 24,565)( 25,564)( 26,563)( 27,562)( 28,571)( 29,573)( 30,572)( 31,568)
( 32,570)( 33,569)( 34,574)( 35,576)( 36,575)( 37,585)( 38,584)( 39,583)
( 40,582)( 41,581)( 42,580)( 43,579)( 44,578)( 45,577)( 46,588)( 47,587)
( 48,586)( 49,594)( 50,593)( 51,592)( 52,591)( 53,590)( 54,589)( 55,598)
( 56,600)( 57,599)( 58,595)( 59,597)( 60,596)( 61,601)( 62,603)( 63,602)
( 64,612)( 65,611)( 66,610)( 67,609)( 68,608)( 69,607)( 70,606)( 71,605)
( 72,604)( 73,615)( 74,614)( 75,613)( 76,621)( 77,620)( 78,619)( 79,618)
( 80,617)( 81,616)( 82,625)( 83,627)( 84,626)( 85,622)( 86,624)( 87,623)
( 88,628)( 89,630)( 90,629)( 91,639)( 92,638)( 93,637)( 94,636)( 95,635)
( 96,634)( 97,633)( 98,632)( 99,631)(100,642)(101,641)(102,640)(103,648)
(104,647)(105,646)(106,645)(107,644)(108,643)(109,436)(110,438)(111,437)
(112,433)(113,435)(114,434)(115,439)(116,441)(117,440)(118,450)(119,449)
(120,448)(121,447)(122,446)(123,445)(124,444)(125,443)(126,442)(127,453)
(128,452)(129,451)(130,459)(131,458)(132,457)(133,456)(134,455)(135,454)
(136,463)(137,465)(138,464)(139,460)(140,462)(141,461)(142,466)(143,468)
(144,467)(145,477)(146,476)(147,475)(148,474)(149,473)(150,472)(151,471)
(152,470)(153,469)(154,480)(155,479)(156,478)(157,486)(158,485)(159,484)
(160,483)(161,482)(162,481)(163,490)(164,492)(165,491)(166,487)(167,489)
(168,488)(169,493)(170,495)(171,494)(172,504)(173,503)(174,502)(175,501)
(176,500)(177,499)(178,498)(179,497)(180,496)(181,507)(182,506)(183,505)
(184,513)(185,512)(186,511)(187,510)(188,509)(189,508)(190,517)(191,519)
(192,518)(193,514)(194,516)(195,515)(196,520)(197,522)(198,521)(199,531)
(200,530)(201,529)(202,528)(203,527)(204,526)(205,525)(206,524)(207,523)
(208,534)(209,533)(210,532)(211,540)(212,539)(213,538)(214,537)(215,536)
(216,535)(217,814)(218,816)(219,815)(220,811)(221,813)(222,812)(223,817)
(224,819)(225,818)(226,828)(227,827)(228,826)(229,825)(230,824)(231,823)
(232,822)(233,821)(234,820)(235,831)(236,830)(237,829)(238,837)(239,836)
(240,835)(241,834)(242,833)(243,832)(244,841)(245,843)(246,842)(247,838)
(248,840)(249,839)(250,844)(251,846)(252,845)(253,855)(254,854)(255,853)
(256,852)(257,851)(258,850)(259,849)(260,848)(261,847)(262,858)(263,857)
(264,856)(265,864)(266,863)(267,862)(268,861)(269,860)(270,859)(271,760)
(272,762)(273,761)(274,757)(275,759)(276,758)(277,763)(278,765)(279,764)
(280,774)(281,773)(282,772)(283,771)(284,770)(285,769)(286,768)(287,767)
(288,766)(289,777)(290,776)(291,775)(292,783)(293,782)(294,781)(295,780)
(296,779)(297,778)(298,787)(299,789)(300,788)(301,784)(302,786)(303,785)
(304,790)(305,792)(306,791)(307,801)(308,800)(309,799)(310,798)(311,797)
(312,796)(313,795)(314,794)(315,793)(316,804)(317,803)(318,802)(319,810)
(320,809)(321,808)(322,807)(323,806)(324,805)(325,706)(326,708)(327,707)
(328,703)(329,705)(330,704)(331,709)(332,711)(333,710)(334,720)(335,719)
(336,718)(337,717)(338,716)(339,715)(340,714)(341,713)(342,712)(343,723)
(344,722)(345,721)(346,729)(347,728)(348,727)(349,726)(350,725)(351,724)
(352,733)(353,735)(354,734)(355,730)(356,732)(357,731)(358,736)(359,738)
(360,737)(361,747)(362,746)(363,745)(364,744)(365,743)(366,742)(367,741)
(368,740)(369,739)(370,750)(371,749)(372,748)(373,756)(374,755)(375,754)
(376,753)(377,752)(378,751)(379,652)(380,654)(381,653)(382,649)(383,651)
(384,650)(385,655)(386,657)(387,656)(388,666)(389,665)(390,664)(391,663)
(392,662)(393,661)(394,660)(395,659)(396,658)(397,669)(398,668)(399,667)
(400,675)(401,674)(402,673)(403,672)(404,671)(405,670)(406,679)(407,681)
(408,680)(409,676)(410,678)(411,677)(412,682)(413,684)(414,683)(415,693)
(416,692)(417,691)(418,690)(419,689)(420,688)(421,687)(422,686)(423,685)
(424,696)(425,695)(426,694)(427,702)(428,701)(429,700)(430,699)(431,698)
(432,697);
s2 := Sym(864)!( 1,109)( 2,111)( 3,110)( 4,124)( 5,126)( 6,125)( 7,132)
( 8,131)( 9,130)( 10,119)( 11,118)( 12,120)( 13,134)( 14,133)( 15,135)
( 16,112)( 17,114)( 18,113)( 19,129)( 20,128)( 21,127)( 22,117)( 23,116)
( 24,115)( 25,122)( 26,121)( 27,123)( 28,136)( 29,138)( 30,137)( 31,151)
( 32,153)( 33,152)( 34,159)( 35,158)( 36,157)( 37,146)( 38,145)( 39,147)
( 40,161)( 41,160)( 42,162)( 43,139)( 44,141)( 45,140)( 46,156)( 47,155)
( 48,154)( 49,144)( 50,143)( 51,142)( 52,149)( 53,148)( 54,150)( 55,163)
( 56,165)( 57,164)( 58,178)( 59,180)( 60,179)( 61,186)( 62,185)( 63,184)
( 64,173)( 65,172)( 66,174)( 67,188)( 68,187)( 69,189)( 70,166)( 71,168)
( 72,167)( 73,183)( 74,182)( 75,181)( 76,171)( 77,170)( 78,169)( 79,176)
( 80,175)( 81,177)( 82,190)( 83,192)( 84,191)( 85,205)( 86,207)( 87,206)
( 88,213)( 89,212)( 90,211)( 91,200)( 92,199)( 93,201)( 94,215)( 95,214)
( 96,216)( 97,193)( 98,195)( 99,194)(100,210)(101,209)(102,208)(103,198)
(104,197)(105,196)(106,203)(107,202)(108,204)(217,352)(218,354)(219,353)
(220,367)(221,369)(222,368)(223,375)(224,374)(225,373)(226,362)(227,361)
(228,363)(229,377)(230,376)(231,378)(232,355)(233,357)(234,356)(235,372)
(236,371)(237,370)(238,360)(239,359)(240,358)(241,365)(242,364)(243,366)
(244,325)(245,327)(246,326)(247,340)(248,342)(249,341)(250,348)(251,347)
(252,346)(253,335)(254,334)(255,336)(256,350)(257,349)(258,351)(259,328)
(260,330)(261,329)(262,345)(263,344)(264,343)(265,333)(266,332)(267,331)
(268,338)(269,337)(270,339)(271,406)(272,408)(273,407)(274,421)(275,423)
(276,422)(277,429)(278,428)(279,427)(280,416)(281,415)(282,417)(283,431)
(284,430)(285,432)(286,409)(287,411)(288,410)(289,426)(290,425)(291,424)
(292,414)(293,413)(294,412)(295,419)(296,418)(297,420)(298,379)(299,381)
(300,380)(301,394)(302,396)(303,395)(304,402)(305,401)(306,400)(307,389)
(308,388)(309,390)(310,404)(311,403)(312,405)(313,382)(314,384)(315,383)
(316,399)(317,398)(318,397)(319,387)(320,386)(321,385)(322,392)(323,391)
(324,393)(433,460)(434,462)(435,461)(436,475)(437,477)(438,476)(439,483)
(440,482)(441,481)(442,470)(443,469)(444,471)(445,485)(446,484)(447,486)
(448,463)(449,465)(450,464)(451,480)(452,479)(453,478)(454,468)(455,467)
(456,466)(457,473)(458,472)(459,474)(487,514)(488,516)(489,515)(490,529)
(491,531)(492,530)(493,537)(494,536)(495,535)(496,524)(497,523)(498,525)
(499,539)(500,538)(501,540)(502,517)(503,519)(504,518)(505,534)(506,533)
(507,532)(508,522)(509,521)(510,520)(511,527)(512,526)(513,528)(542,543)
(544,556)(545,558)(546,557)(547,564)(548,563)(549,562)(550,551)(553,566)
(554,565)(555,567)(559,561)(569,570)(571,583)(572,585)(573,584)(574,591)
(575,590)(576,589)(577,578)(580,593)(581,592)(582,594)(586,588)(596,597)
(598,610)(599,612)(600,611)(601,618)(602,617)(603,616)(604,605)(607,620)
(608,619)(609,621)(613,615)(623,624)(625,637)(626,639)(627,638)(628,645)
(629,644)(630,643)(631,632)(634,647)(635,646)(636,648)(640,642)(650,651)
(652,664)(653,666)(654,665)(655,672)(656,671)(657,670)(658,659)(661,674)
(662,673)(663,675)(667,669)(677,678)(679,691)(680,693)(681,692)(682,699)
(683,698)(684,697)(685,686)(688,701)(689,700)(690,702)(694,696)(704,705)
(706,718)(707,720)(708,719)(709,726)(710,725)(711,724)(712,713)(715,728)
(716,727)(717,729)(721,723)(731,732)(733,745)(734,747)(735,746)(736,753)
(737,752)(738,751)(739,740)(742,755)(743,754)(744,756)(748,750)(757,784)
(758,786)(759,785)(760,799)(761,801)(762,800)(763,807)(764,806)(765,805)
(766,794)(767,793)(768,795)(769,809)(770,808)(771,810)(772,787)(773,789)
(774,788)(775,804)(776,803)(777,802)(778,792)(779,791)(780,790)(781,797)
(782,796)(783,798)(811,838)(812,840)(813,839)(814,853)(815,855)(816,854)
(817,861)(818,860)(819,859)(820,848)(821,847)(822,849)(823,863)(824,862)
(825,864)(826,841)(827,843)(828,842)(829,858)(830,857)(831,856)(832,846)
(833,845)(834,844)(835,851)(836,850)(837,852);
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*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*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*s1*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