Polytope of Type {12,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*1728x
if this polytope has a name.
Group : SmallGroup(1728,33667)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 36, 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 : {12,12}*864l
3-fold quotients : {12,8}*576b
4-fold quotients : {6,12}*432i
6-fold quotients : {12,4}*288
8-fold quotients : {6,12}*216c
9-fold quotients : {4,24}*192b
12-fold quotients : {6,4}*144
18-fold quotients : {4,12}*96a
24-fold quotients : {6,4}*72
27-fold quotients : {4,8}*64b
36-fold quotients : {2,12}*48, {4,6}*48a
54-fold quotients : {4,4}*32
72-fold quotients : {2,6}*24
108-fold quotients : {2,4}*16, {4,2}*16
144-fold quotients : {2,3}*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)( 10,334)( 11,336)( 12,335)( 13,340)( 14,342)( 15,341)( 16,337)
( 17,339)( 18,338)( 19,343)( 20,345)( 21,344)( 22,349)( 23,351)( 24,350)
( 25,346)( 26,348)( 27,347)( 28,352)( 29,354)( 30,353)( 31,358)( 32,360)
( 33,359)( 34,355)( 35,357)( 36,356)( 37,361)( 38,363)( 39,362)( 40,367)
( 41,369)( 42,368)( 43,364)( 44,366)( 45,365)( 46,370)( 47,372)( 48,371)
( 49,376)( 50,378)( 51,377)( 52,373)( 53,375)( 54,374)( 55,379)( 56,381)
( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)( 64,388)
( 65,390)( 66,389)( 67,394)( 68,396)( 69,395)( 70,391)( 71,393)( 72,392)
( 73,397)( 74,399)( 75,398)( 76,403)( 77,405)( 78,404)( 79,400)( 80,402)
( 81,401)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)( 88,409)
( 89,411)( 90,410)( 91,415)( 92,417)( 93,416)( 94,421)( 95,423)( 96,422)
( 97,418)( 98,420)( 99,419)(100,424)(101,426)(102,425)(103,430)(104,432)
(105,431)(106,427)(107,429)(108,428)(109,217)(110,219)(111,218)(112,223)
(113,225)(114,224)(115,220)(116,222)(117,221)(118,226)(119,228)(120,227)
(121,232)(122,234)(123,233)(124,229)(125,231)(126,230)(127,235)(128,237)
(129,236)(130,241)(131,243)(132,242)(133,238)(134,240)(135,239)(136,244)
(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)(144,248)
(145,253)(146,255)(147,254)(148,259)(149,261)(150,260)(151,256)(152,258)
(153,257)(154,262)(155,264)(156,263)(157,268)(158,270)(159,269)(160,265)
(161,267)(162,266)(163,271)(164,273)(165,272)(166,277)(167,279)(168,278)
(169,274)(170,276)(171,275)(172,280)(173,282)(174,281)(175,286)(176,288)
(177,287)(178,283)(179,285)(180,284)(181,289)(182,291)(183,290)(184,295)
(185,297)(186,296)(187,292)(188,294)(189,293)(190,298)(191,300)(192,299)
(193,304)(194,306)(195,305)(196,301)(197,303)(198,302)(199,307)(200,309)
(201,308)(202,313)(203,315)(204,314)(205,310)(206,312)(207,311)(208,316)
(209,318)(210,317)(211,322)(212,324)(213,323)(214,319)(215,321)(216,320)
(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)(440,762)
(441,761)(442,766)(443,768)(444,767)(445,772)(446,774)(447,773)(448,769)
(449,771)(450,770)(451,775)(452,777)(453,776)(454,781)(455,783)(456,782)
(457,778)(458,780)(459,779)(460,784)(461,786)(462,785)(463,790)(464,792)
(465,791)(466,787)(467,789)(468,788)(469,793)(470,795)(471,794)(472,799)
(473,801)(474,800)(475,796)(476,798)(477,797)(478,802)(479,804)(480,803)
(481,808)(482,810)(483,809)(484,805)(485,807)(486,806)(487,811)(488,813)
(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)(496,820)
(497,822)(498,821)(499,826)(500,828)(501,827)(502,823)(503,825)(504,824)
(505,829)(506,831)(507,830)(508,835)(509,837)(510,836)(511,832)(512,834)
(513,833)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)(520,841)
(521,843)(522,842)(523,847)(524,849)(525,848)(526,853)(527,855)(528,854)
(529,850)(530,852)(531,851)(532,856)(533,858)(534,857)(535,862)(536,864)
(537,863)(538,859)(539,861)(540,860)(541,649)(542,651)(543,650)(544,655)
(545,657)(546,656)(547,652)(548,654)(549,653)(550,658)(551,660)(552,659)
(553,664)(554,666)(555,665)(556,661)(557,663)(558,662)(559,667)(560,669)
(561,668)(562,673)(563,675)(564,674)(565,670)(566,672)(567,671)(568,676)
(569,678)(570,677)(571,682)(572,684)(573,683)(574,679)(575,681)(576,680)
(577,685)(578,687)(579,686)(580,691)(581,693)(582,692)(583,688)(584,690)
(585,689)(586,694)(587,696)(588,695)(589,700)(590,702)(591,701)(592,697)
(593,699)(594,698)(595,703)(596,705)(597,704)(598,709)(599,711)(600,710)
(601,706)(602,708)(603,707)(604,712)(605,714)(606,713)(607,718)(608,720)
(609,719)(610,715)(611,717)(612,716)(613,721)(614,723)(615,722)(616,727)
(617,729)(618,728)(619,724)(620,726)(621,725)(622,730)(623,732)(624,731)
(625,736)(626,738)(627,737)(628,733)(629,735)(630,734)(631,739)(632,741)
(633,740)(634,745)(635,747)(636,746)(637,742)(638,744)(639,743)(640,748)
(641,750)(642,749)(643,754)(644,756)(645,755)(646,751)(647,753)(648,752);;
s1 := ( 1,542)( 2,541)( 3,543)( 4,546)( 5,545)( 6,544)( 7,547)( 8,549)
( 9,548)( 10,560)( 11,559)( 12,561)( 13,564)( 14,563)( 15,562)( 16,565)
( 17,567)( 18,566)( 19,551)( 20,550)( 21,552)( 22,555)( 23,554)( 24,553)
( 25,556)( 26,558)( 27,557)( 28,569)( 29,568)( 30,570)( 31,573)( 32,572)
( 33,571)( 34,574)( 35,576)( 36,575)( 37,587)( 38,586)( 39,588)( 40,591)
( 41,590)( 42,589)( 43,592)( 44,594)( 45,593)( 46,578)( 47,577)( 48,579)
( 49,582)( 50,581)( 51,580)( 52,583)( 53,585)( 54,584)( 55,596)( 56,595)
( 57,597)( 58,600)( 59,599)( 60,598)( 61,601)( 62,603)( 63,602)( 64,614)
( 65,613)( 66,615)( 67,618)( 68,617)( 69,616)( 70,619)( 71,621)( 72,620)
( 73,605)( 74,604)( 75,606)( 76,609)( 77,608)( 78,607)( 79,610)( 80,612)
( 81,611)( 82,623)( 83,622)( 84,624)( 85,627)( 86,626)( 87,625)( 88,628)
( 89,630)( 90,629)( 91,641)( 92,640)( 93,642)( 94,645)( 95,644)( 96,643)
( 97,646)( 98,648)( 99,647)(100,632)(101,631)(102,633)(103,636)(104,635)
(105,634)(106,637)(107,639)(108,638)(109,434)(110,433)(111,435)(112,438)
(113,437)(114,436)(115,439)(116,441)(117,440)(118,452)(119,451)(120,453)
(121,456)(122,455)(123,454)(124,457)(125,459)(126,458)(127,443)(128,442)
(129,444)(130,447)(131,446)(132,445)(133,448)(134,450)(135,449)(136,461)
(137,460)(138,462)(139,465)(140,464)(141,463)(142,466)(143,468)(144,467)
(145,479)(146,478)(147,480)(148,483)(149,482)(150,481)(151,484)(152,486)
(153,485)(154,470)(155,469)(156,471)(157,474)(158,473)(159,472)(160,475)
(161,477)(162,476)(163,488)(164,487)(165,489)(166,492)(167,491)(168,490)
(169,493)(170,495)(171,494)(172,506)(173,505)(174,507)(175,510)(176,509)
(177,508)(178,511)(179,513)(180,512)(181,497)(182,496)(183,498)(184,501)
(185,500)(186,499)(187,502)(188,504)(189,503)(190,515)(191,514)(192,516)
(193,519)(194,518)(195,517)(196,520)(197,522)(198,521)(199,533)(200,532)
(201,534)(202,537)(203,536)(204,535)(205,538)(206,540)(207,539)(208,524)
(209,523)(210,525)(211,528)(212,527)(213,526)(214,529)(215,531)(216,530)
(217,812)(218,811)(219,813)(220,816)(221,815)(222,814)(223,817)(224,819)
(225,818)(226,830)(227,829)(228,831)(229,834)(230,833)(231,832)(232,835)
(233,837)(234,836)(235,821)(236,820)(237,822)(238,825)(239,824)(240,823)
(241,826)(242,828)(243,827)(244,839)(245,838)(246,840)(247,843)(248,842)
(249,841)(250,844)(251,846)(252,845)(253,857)(254,856)(255,858)(256,861)
(257,860)(258,859)(259,862)(260,864)(261,863)(262,848)(263,847)(264,849)
(265,852)(266,851)(267,850)(268,853)(269,855)(270,854)(271,758)(272,757)
(273,759)(274,762)(275,761)(276,760)(277,763)(278,765)(279,764)(280,776)
(281,775)(282,777)(283,780)(284,779)(285,778)(286,781)(287,783)(288,782)
(289,767)(290,766)(291,768)(292,771)(293,770)(294,769)(295,772)(296,774)
(297,773)(298,785)(299,784)(300,786)(301,789)(302,788)(303,787)(304,790)
(305,792)(306,791)(307,803)(308,802)(309,804)(310,807)(311,806)(312,805)
(313,808)(314,810)(315,809)(316,794)(317,793)(318,795)(319,798)(320,797)
(321,796)(322,799)(323,801)(324,800)(325,704)(326,703)(327,705)(328,708)
(329,707)(330,706)(331,709)(332,711)(333,710)(334,722)(335,721)(336,723)
(337,726)(338,725)(339,724)(340,727)(341,729)(342,728)(343,713)(344,712)
(345,714)(346,717)(347,716)(348,715)(349,718)(350,720)(351,719)(352,731)
(353,730)(354,732)(355,735)(356,734)(357,733)(358,736)(359,738)(360,737)
(361,749)(362,748)(363,750)(364,753)(365,752)(366,751)(367,754)(368,756)
(369,755)(370,740)(371,739)(372,741)(373,744)(374,743)(375,742)(376,745)
(377,747)(378,746)(379,650)(380,649)(381,651)(382,654)(383,653)(384,652)
(385,655)(386,657)(387,656)(388,668)(389,667)(390,669)(391,672)(392,671)
(393,670)(394,673)(395,675)(396,674)(397,659)(398,658)(399,660)(400,663)
(401,662)(402,661)(403,664)(404,666)(405,665)(406,677)(407,676)(408,678)
(409,681)(410,680)(411,679)(412,682)(413,684)(414,683)(415,695)(416,694)
(417,696)(418,699)(419,698)(420,697)(421,700)(422,702)(423,701)(424,686)
(425,685)(426,687)(427,690)(428,689)(429,688)(430,691)(431,693)(432,692);;
s2 := ( 1,226)( 2,233)( 3,231)( 4,232)( 5,230)( 6,228)( 7,229)( 8,227)
( 9,234)( 10,217)( 11,224)( 12,222)( 13,223)( 14,221)( 15,219)( 16,220)
( 17,218)( 18,225)( 19,235)( 20,242)( 21,240)( 22,241)( 23,239)( 24,237)
( 25,238)( 26,236)( 27,243)( 28,253)( 29,260)( 30,258)( 31,259)( 32,257)
( 33,255)( 34,256)( 35,254)( 36,261)( 37,244)( 38,251)( 39,249)( 40,250)
( 41,248)( 42,246)( 43,247)( 44,245)( 45,252)( 46,262)( 47,269)( 48,267)
( 49,268)( 50,266)( 51,264)( 52,265)( 53,263)( 54,270)( 55,307)( 56,314)
( 57,312)( 58,313)( 59,311)( 60,309)( 61,310)( 62,308)( 63,315)( 64,298)
( 65,305)( 66,303)( 67,304)( 68,302)( 69,300)( 70,301)( 71,299)( 72,306)
( 73,316)( 74,323)( 75,321)( 76,322)( 77,320)( 78,318)( 79,319)( 80,317)
( 81,324)( 82,280)( 83,287)( 84,285)( 85,286)( 86,284)( 87,282)( 88,283)
( 89,281)( 90,288)( 91,271)( 92,278)( 93,276)( 94,277)( 95,275)( 96,273)
( 97,274)( 98,272)( 99,279)(100,289)(101,296)(102,294)(103,295)(104,293)
(105,291)(106,292)(107,290)(108,297)(109,334)(110,341)(111,339)(112,340)
(113,338)(114,336)(115,337)(116,335)(117,342)(118,325)(119,332)(120,330)
(121,331)(122,329)(123,327)(124,328)(125,326)(126,333)(127,343)(128,350)
(129,348)(130,349)(131,347)(132,345)(133,346)(134,344)(135,351)(136,361)
(137,368)(138,366)(139,367)(140,365)(141,363)(142,364)(143,362)(144,369)
(145,352)(146,359)(147,357)(148,358)(149,356)(150,354)(151,355)(152,353)
(153,360)(154,370)(155,377)(156,375)(157,376)(158,374)(159,372)(160,373)
(161,371)(162,378)(163,415)(164,422)(165,420)(166,421)(167,419)(168,417)
(169,418)(170,416)(171,423)(172,406)(173,413)(174,411)(175,412)(176,410)
(177,408)(178,409)(179,407)(180,414)(181,424)(182,431)(183,429)(184,430)
(185,428)(186,426)(187,427)(188,425)(189,432)(190,388)(191,395)(192,393)
(193,394)(194,392)(195,390)(196,391)(197,389)(198,396)(199,379)(200,386)
(201,384)(202,385)(203,383)(204,381)(205,382)(206,380)(207,387)(208,397)
(209,404)(210,402)(211,403)(212,401)(213,399)(214,400)(215,398)(216,405)
(433,793)(434,800)(435,798)(436,799)(437,797)(438,795)(439,796)(440,794)
(441,801)(442,784)(443,791)(444,789)(445,790)(446,788)(447,786)(448,787)
(449,785)(450,792)(451,802)(452,809)(453,807)(454,808)(455,806)(456,804)
(457,805)(458,803)(459,810)(460,766)(461,773)(462,771)(463,772)(464,770)
(465,768)(466,769)(467,767)(468,774)(469,757)(470,764)(471,762)(472,763)
(473,761)(474,759)(475,760)(476,758)(477,765)(478,775)(479,782)(480,780)
(481,781)(482,779)(483,777)(484,778)(485,776)(486,783)(487,820)(488,827)
(489,825)(490,826)(491,824)(492,822)(493,823)(494,821)(495,828)(496,811)
(497,818)(498,816)(499,817)(500,815)(501,813)(502,814)(503,812)(504,819)
(505,829)(506,836)(507,834)(508,835)(509,833)(510,831)(511,832)(512,830)
(513,837)(514,847)(515,854)(516,852)(517,853)(518,851)(519,849)(520,850)
(521,848)(522,855)(523,838)(524,845)(525,843)(526,844)(527,842)(528,840)
(529,841)(530,839)(531,846)(532,856)(533,863)(534,861)(535,862)(536,860)
(537,858)(538,859)(539,857)(540,864)(541,658)(542,665)(543,663)(544,664)
(545,662)(546,660)(547,661)(548,659)(549,666)(550,649)(551,656)(552,654)
(553,655)(554,653)(555,651)(556,652)(557,650)(558,657)(559,667)(560,674)
(561,672)(562,673)(563,671)(564,669)(565,670)(566,668)(567,675)(568,685)
(569,692)(570,690)(571,691)(572,689)(573,687)(574,688)(575,686)(576,693)
(577,676)(578,683)(579,681)(580,682)(581,680)(582,678)(583,679)(584,677)
(585,684)(586,694)(587,701)(588,699)(589,700)(590,698)(591,696)(592,697)
(593,695)(594,702)(595,739)(596,746)(597,744)(598,745)(599,743)(600,741)
(601,742)(602,740)(603,747)(604,730)(605,737)(606,735)(607,736)(608,734)
(609,732)(610,733)(611,731)(612,738)(613,748)(614,755)(615,753)(616,754)
(617,752)(618,750)(619,751)(620,749)(621,756)(622,712)(623,719)(624,717)
(625,718)(626,716)(627,714)(628,715)(629,713)(630,720)(631,703)(632,710)
(633,708)(634,709)(635,707)(636,705)(637,706)(638,704)(639,711)(640,721)
(641,728)(642,726)(643,727)(644,725)(645,723)(646,724)(647,722)(648,729);;
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*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*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*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)( 10,334)( 11,336)( 12,335)( 13,340)( 14,342)( 15,341)
( 16,337)( 17,339)( 18,338)( 19,343)( 20,345)( 21,344)( 22,349)( 23,351)
( 24,350)( 25,346)( 26,348)( 27,347)( 28,352)( 29,354)( 30,353)( 31,358)
( 32,360)( 33,359)( 34,355)( 35,357)( 36,356)( 37,361)( 38,363)( 39,362)
( 40,367)( 41,369)( 42,368)( 43,364)( 44,366)( 45,365)( 46,370)( 47,372)
( 48,371)( 49,376)( 50,378)( 51,377)( 52,373)( 53,375)( 54,374)( 55,379)
( 56,381)( 57,380)( 58,385)( 59,387)( 60,386)( 61,382)( 62,384)( 63,383)
( 64,388)( 65,390)( 66,389)( 67,394)( 68,396)( 69,395)( 70,391)( 71,393)
( 72,392)( 73,397)( 74,399)( 75,398)( 76,403)( 77,405)( 78,404)( 79,400)
( 80,402)( 81,401)( 82,406)( 83,408)( 84,407)( 85,412)( 86,414)( 87,413)
( 88,409)( 89,411)( 90,410)( 91,415)( 92,417)( 93,416)( 94,421)( 95,423)
( 96,422)( 97,418)( 98,420)( 99,419)(100,424)(101,426)(102,425)(103,430)
(104,432)(105,431)(106,427)(107,429)(108,428)(109,217)(110,219)(111,218)
(112,223)(113,225)(114,224)(115,220)(116,222)(117,221)(118,226)(119,228)
(120,227)(121,232)(122,234)(123,233)(124,229)(125,231)(126,230)(127,235)
(128,237)(129,236)(130,241)(131,243)(132,242)(133,238)(134,240)(135,239)
(136,244)(137,246)(138,245)(139,250)(140,252)(141,251)(142,247)(143,249)
(144,248)(145,253)(146,255)(147,254)(148,259)(149,261)(150,260)(151,256)
(152,258)(153,257)(154,262)(155,264)(156,263)(157,268)(158,270)(159,269)
(160,265)(161,267)(162,266)(163,271)(164,273)(165,272)(166,277)(167,279)
(168,278)(169,274)(170,276)(171,275)(172,280)(173,282)(174,281)(175,286)
(176,288)(177,287)(178,283)(179,285)(180,284)(181,289)(182,291)(183,290)
(184,295)(185,297)(186,296)(187,292)(188,294)(189,293)(190,298)(191,300)
(192,299)(193,304)(194,306)(195,305)(196,301)(197,303)(198,302)(199,307)
(200,309)(201,308)(202,313)(203,315)(204,314)(205,310)(206,312)(207,311)
(208,316)(209,318)(210,317)(211,322)(212,324)(213,323)(214,319)(215,321)
(216,320)(433,757)(434,759)(435,758)(436,763)(437,765)(438,764)(439,760)
(440,762)(441,761)(442,766)(443,768)(444,767)(445,772)(446,774)(447,773)
(448,769)(449,771)(450,770)(451,775)(452,777)(453,776)(454,781)(455,783)
(456,782)(457,778)(458,780)(459,779)(460,784)(461,786)(462,785)(463,790)
(464,792)(465,791)(466,787)(467,789)(468,788)(469,793)(470,795)(471,794)
(472,799)(473,801)(474,800)(475,796)(476,798)(477,797)(478,802)(479,804)
(480,803)(481,808)(482,810)(483,809)(484,805)(485,807)(486,806)(487,811)
(488,813)(489,812)(490,817)(491,819)(492,818)(493,814)(494,816)(495,815)
(496,820)(497,822)(498,821)(499,826)(500,828)(501,827)(502,823)(503,825)
(504,824)(505,829)(506,831)(507,830)(508,835)(509,837)(510,836)(511,832)
(512,834)(513,833)(514,838)(515,840)(516,839)(517,844)(518,846)(519,845)
(520,841)(521,843)(522,842)(523,847)(524,849)(525,848)(526,853)(527,855)
(528,854)(529,850)(530,852)(531,851)(532,856)(533,858)(534,857)(535,862)
(536,864)(537,863)(538,859)(539,861)(540,860)(541,649)(542,651)(543,650)
(544,655)(545,657)(546,656)(547,652)(548,654)(549,653)(550,658)(551,660)
(552,659)(553,664)(554,666)(555,665)(556,661)(557,663)(558,662)(559,667)
(560,669)(561,668)(562,673)(563,675)(564,674)(565,670)(566,672)(567,671)
(568,676)(569,678)(570,677)(571,682)(572,684)(573,683)(574,679)(575,681)
(576,680)(577,685)(578,687)(579,686)(580,691)(581,693)(582,692)(583,688)
(584,690)(585,689)(586,694)(587,696)(588,695)(589,700)(590,702)(591,701)
(592,697)(593,699)(594,698)(595,703)(596,705)(597,704)(598,709)(599,711)
(600,710)(601,706)(602,708)(603,707)(604,712)(605,714)(606,713)(607,718)
(608,720)(609,719)(610,715)(611,717)(612,716)(613,721)(614,723)(615,722)
(616,727)(617,729)(618,728)(619,724)(620,726)(621,725)(622,730)(623,732)
(624,731)(625,736)(626,738)(627,737)(628,733)(629,735)(630,734)(631,739)
(632,741)(633,740)(634,745)(635,747)(636,746)(637,742)(638,744)(639,743)
(640,748)(641,750)(642,749)(643,754)(644,756)(645,755)(646,751)(647,753)
(648,752);
s1 := Sym(864)!( 1,542)( 2,541)( 3,543)( 4,546)( 5,545)( 6,544)( 7,547)
( 8,549)( 9,548)( 10,560)( 11,559)( 12,561)( 13,564)( 14,563)( 15,562)
( 16,565)( 17,567)( 18,566)( 19,551)( 20,550)( 21,552)( 22,555)( 23,554)
( 24,553)( 25,556)( 26,558)( 27,557)( 28,569)( 29,568)( 30,570)( 31,573)
( 32,572)( 33,571)( 34,574)( 35,576)( 36,575)( 37,587)( 38,586)( 39,588)
( 40,591)( 41,590)( 42,589)( 43,592)( 44,594)( 45,593)( 46,578)( 47,577)
( 48,579)( 49,582)( 50,581)( 51,580)( 52,583)( 53,585)( 54,584)( 55,596)
( 56,595)( 57,597)( 58,600)( 59,599)( 60,598)( 61,601)( 62,603)( 63,602)
( 64,614)( 65,613)( 66,615)( 67,618)( 68,617)( 69,616)( 70,619)( 71,621)
( 72,620)( 73,605)( 74,604)( 75,606)( 76,609)( 77,608)( 78,607)( 79,610)
( 80,612)( 81,611)( 82,623)( 83,622)( 84,624)( 85,627)( 86,626)( 87,625)
( 88,628)( 89,630)( 90,629)( 91,641)( 92,640)( 93,642)( 94,645)( 95,644)
( 96,643)( 97,646)( 98,648)( 99,647)(100,632)(101,631)(102,633)(103,636)
(104,635)(105,634)(106,637)(107,639)(108,638)(109,434)(110,433)(111,435)
(112,438)(113,437)(114,436)(115,439)(116,441)(117,440)(118,452)(119,451)
(120,453)(121,456)(122,455)(123,454)(124,457)(125,459)(126,458)(127,443)
(128,442)(129,444)(130,447)(131,446)(132,445)(133,448)(134,450)(135,449)
(136,461)(137,460)(138,462)(139,465)(140,464)(141,463)(142,466)(143,468)
(144,467)(145,479)(146,478)(147,480)(148,483)(149,482)(150,481)(151,484)
(152,486)(153,485)(154,470)(155,469)(156,471)(157,474)(158,473)(159,472)
(160,475)(161,477)(162,476)(163,488)(164,487)(165,489)(166,492)(167,491)
(168,490)(169,493)(170,495)(171,494)(172,506)(173,505)(174,507)(175,510)
(176,509)(177,508)(178,511)(179,513)(180,512)(181,497)(182,496)(183,498)
(184,501)(185,500)(186,499)(187,502)(188,504)(189,503)(190,515)(191,514)
(192,516)(193,519)(194,518)(195,517)(196,520)(197,522)(198,521)(199,533)
(200,532)(201,534)(202,537)(203,536)(204,535)(205,538)(206,540)(207,539)
(208,524)(209,523)(210,525)(211,528)(212,527)(213,526)(214,529)(215,531)
(216,530)(217,812)(218,811)(219,813)(220,816)(221,815)(222,814)(223,817)
(224,819)(225,818)(226,830)(227,829)(228,831)(229,834)(230,833)(231,832)
(232,835)(233,837)(234,836)(235,821)(236,820)(237,822)(238,825)(239,824)
(240,823)(241,826)(242,828)(243,827)(244,839)(245,838)(246,840)(247,843)
(248,842)(249,841)(250,844)(251,846)(252,845)(253,857)(254,856)(255,858)
(256,861)(257,860)(258,859)(259,862)(260,864)(261,863)(262,848)(263,847)
(264,849)(265,852)(266,851)(267,850)(268,853)(269,855)(270,854)(271,758)
(272,757)(273,759)(274,762)(275,761)(276,760)(277,763)(278,765)(279,764)
(280,776)(281,775)(282,777)(283,780)(284,779)(285,778)(286,781)(287,783)
(288,782)(289,767)(290,766)(291,768)(292,771)(293,770)(294,769)(295,772)
(296,774)(297,773)(298,785)(299,784)(300,786)(301,789)(302,788)(303,787)
(304,790)(305,792)(306,791)(307,803)(308,802)(309,804)(310,807)(311,806)
(312,805)(313,808)(314,810)(315,809)(316,794)(317,793)(318,795)(319,798)
(320,797)(321,796)(322,799)(323,801)(324,800)(325,704)(326,703)(327,705)
(328,708)(329,707)(330,706)(331,709)(332,711)(333,710)(334,722)(335,721)
(336,723)(337,726)(338,725)(339,724)(340,727)(341,729)(342,728)(343,713)
(344,712)(345,714)(346,717)(347,716)(348,715)(349,718)(350,720)(351,719)
(352,731)(353,730)(354,732)(355,735)(356,734)(357,733)(358,736)(359,738)
(360,737)(361,749)(362,748)(363,750)(364,753)(365,752)(366,751)(367,754)
(368,756)(369,755)(370,740)(371,739)(372,741)(373,744)(374,743)(375,742)
(376,745)(377,747)(378,746)(379,650)(380,649)(381,651)(382,654)(383,653)
(384,652)(385,655)(386,657)(387,656)(388,668)(389,667)(390,669)(391,672)
(392,671)(393,670)(394,673)(395,675)(396,674)(397,659)(398,658)(399,660)
(400,663)(401,662)(402,661)(403,664)(404,666)(405,665)(406,677)(407,676)
(408,678)(409,681)(410,680)(411,679)(412,682)(413,684)(414,683)(415,695)
(416,694)(417,696)(418,699)(419,698)(420,697)(421,700)(422,702)(423,701)
(424,686)(425,685)(426,687)(427,690)(428,689)(429,688)(430,691)(431,693)
(432,692);
s2 := Sym(864)!( 1,226)( 2,233)( 3,231)( 4,232)( 5,230)( 6,228)( 7,229)
( 8,227)( 9,234)( 10,217)( 11,224)( 12,222)( 13,223)( 14,221)( 15,219)
( 16,220)( 17,218)( 18,225)( 19,235)( 20,242)( 21,240)( 22,241)( 23,239)
( 24,237)( 25,238)( 26,236)( 27,243)( 28,253)( 29,260)( 30,258)( 31,259)
( 32,257)( 33,255)( 34,256)( 35,254)( 36,261)( 37,244)( 38,251)( 39,249)
( 40,250)( 41,248)( 42,246)( 43,247)( 44,245)( 45,252)( 46,262)( 47,269)
( 48,267)( 49,268)( 50,266)( 51,264)( 52,265)( 53,263)( 54,270)( 55,307)
( 56,314)( 57,312)( 58,313)( 59,311)( 60,309)( 61,310)( 62,308)( 63,315)
( 64,298)( 65,305)( 66,303)( 67,304)( 68,302)( 69,300)( 70,301)( 71,299)
( 72,306)( 73,316)( 74,323)( 75,321)( 76,322)( 77,320)( 78,318)( 79,319)
( 80,317)( 81,324)( 82,280)( 83,287)( 84,285)( 85,286)( 86,284)( 87,282)
( 88,283)( 89,281)( 90,288)( 91,271)( 92,278)( 93,276)( 94,277)( 95,275)
( 96,273)( 97,274)( 98,272)( 99,279)(100,289)(101,296)(102,294)(103,295)
(104,293)(105,291)(106,292)(107,290)(108,297)(109,334)(110,341)(111,339)
(112,340)(113,338)(114,336)(115,337)(116,335)(117,342)(118,325)(119,332)
(120,330)(121,331)(122,329)(123,327)(124,328)(125,326)(126,333)(127,343)
(128,350)(129,348)(130,349)(131,347)(132,345)(133,346)(134,344)(135,351)
(136,361)(137,368)(138,366)(139,367)(140,365)(141,363)(142,364)(143,362)
(144,369)(145,352)(146,359)(147,357)(148,358)(149,356)(150,354)(151,355)
(152,353)(153,360)(154,370)(155,377)(156,375)(157,376)(158,374)(159,372)
(160,373)(161,371)(162,378)(163,415)(164,422)(165,420)(166,421)(167,419)
(168,417)(169,418)(170,416)(171,423)(172,406)(173,413)(174,411)(175,412)
(176,410)(177,408)(178,409)(179,407)(180,414)(181,424)(182,431)(183,429)
(184,430)(185,428)(186,426)(187,427)(188,425)(189,432)(190,388)(191,395)
(192,393)(193,394)(194,392)(195,390)(196,391)(197,389)(198,396)(199,379)
(200,386)(201,384)(202,385)(203,383)(204,381)(205,382)(206,380)(207,387)
(208,397)(209,404)(210,402)(211,403)(212,401)(213,399)(214,400)(215,398)
(216,405)(433,793)(434,800)(435,798)(436,799)(437,797)(438,795)(439,796)
(440,794)(441,801)(442,784)(443,791)(444,789)(445,790)(446,788)(447,786)
(448,787)(449,785)(450,792)(451,802)(452,809)(453,807)(454,808)(455,806)
(456,804)(457,805)(458,803)(459,810)(460,766)(461,773)(462,771)(463,772)
(464,770)(465,768)(466,769)(467,767)(468,774)(469,757)(470,764)(471,762)
(472,763)(473,761)(474,759)(475,760)(476,758)(477,765)(478,775)(479,782)
(480,780)(481,781)(482,779)(483,777)(484,778)(485,776)(486,783)(487,820)
(488,827)(489,825)(490,826)(491,824)(492,822)(493,823)(494,821)(495,828)
(496,811)(497,818)(498,816)(499,817)(500,815)(501,813)(502,814)(503,812)
(504,819)(505,829)(506,836)(507,834)(508,835)(509,833)(510,831)(511,832)
(512,830)(513,837)(514,847)(515,854)(516,852)(517,853)(518,851)(519,849)
(520,850)(521,848)(522,855)(523,838)(524,845)(525,843)(526,844)(527,842)
(528,840)(529,841)(530,839)(531,846)(532,856)(533,863)(534,861)(535,862)
(536,860)(537,858)(538,859)(539,857)(540,864)(541,658)(542,665)(543,663)
(544,664)(545,662)(546,660)(547,661)(548,659)(549,666)(550,649)(551,656)
(552,654)(553,655)(554,653)(555,651)(556,652)(557,650)(558,657)(559,667)
(560,674)(561,672)(562,673)(563,671)(564,669)(565,670)(566,668)(567,675)
(568,685)(569,692)(570,690)(571,691)(572,689)(573,687)(574,688)(575,686)
(576,693)(577,676)(578,683)(579,681)(580,682)(581,680)(582,678)(583,679)
(584,677)(585,684)(586,694)(587,701)(588,699)(589,700)(590,698)(591,696)
(592,697)(593,695)(594,702)(595,739)(596,746)(597,744)(598,745)(599,743)
(600,741)(601,742)(602,740)(603,747)(604,730)(605,737)(606,735)(607,736)
(608,734)(609,732)(610,733)(611,731)(612,738)(613,748)(614,755)(615,753)
(616,754)(617,752)(618,750)(619,751)(620,749)(621,756)(622,712)(623,719)
(624,717)(625,718)(626,716)(627,714)(628,715)(629,713)(630,720)(631,703)
(632,710)(633,708)(634,709)(635,707)(636,705)(637,706)(638,704)(639,711)
(640,721)(641,728)(642,726)(643,727)(644,725)(645,723)(646,724)(647,722)
(648,729);
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, s2*s0*s1*s2*s0*s1*s0*s1*s2*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*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1 >;
References : None.
to this polytope