Polytope of Type {12,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*1728m
if this polytope has a name.
Group : SmallGroup(1728,12762)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 36, 432, 72
Order of s0s1s2 : 8
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}*864f
3-fold quotients : {12,8}*576b
4-fold quotients : {6,12}*432f
6-fold quotients : {12,4}*288
8-fold quotients : {6,12}*216b
12-fold quotients : {6,4}*144
24-fold quotients : {6,4}*72
27-fold quotients : {4,8}*64b
54-fold quotients : {4,4}*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)(109,217)(110,218)(111,219)(112,225)
(113,223)(114,224)(115,221)(116,222)(117,220)(118,237)(119,235)(120,236)
(121,242)(122,243)(123,241)(124,238)(125,239)(126,240)(127,227)(128,228)
(129,226)(130,232)(131,233)(132,234)(133,231)(134,229)(135,230)(136,244)
(137,245)(138,246)(139,252)(140,250)(141,251)(142,248)(143,249)(144,247)
(145,264)(146,262)(147,263)(148,269)(149,270)(150,268)(151,265)(152,266)
(153,267)(154,254)(155,255)(156,253)(157,259)(158,260)(159,261)(160,258)
(161,256)(162,257)(163,271)(164,272)(165,273)(166,279)(167,277)(168,278)
(169,275)(170,276)(171,274)(172,291)(173,289)(174,290)(175,296)(176,297)
(177,295)(178,292)(179,293)(180,294)(181,281)(182,282)(183,280)(184,286)
(185,287)(186,288)(187,285)(188,283)(189,284)(190,298)(191,299)(192,300)
(193,306)(194,304)(195,305)(196,302)(197,303)(198,301)(199,318)(200,316)
(201,317)(202,323)(203,324)(204,322)(205,319)(206,320)(207,321)(208,308)
(209,309)(210,307)(211,313)(212,314)(213,315)(214,312)(215,310)(216,311)
(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)(541,649)(542,650)(543,651)(544,657)
(545,655)(546,656)(547,653)(548,654)(549,652)(550,669)(551,667)(552,668)
(553,674)(554,675)(555,673)(556,670)(557,671)(558,672)(559,659)(560,660)
(561,658)(562,664)(563,665)(564,666)(565,663)(566,661)(567,662)(568,676)
(569,677)(570,678)(571,684)(572,682)(573,683)(574,680)(575,681)(576,679)
(577,696)(578,694)(579,695)(580,701)(581,702)(582,700)(583,697)(584,698)
(585,699)(586,686)(587,687)(588,685)(589,691)(590,692)(591,693)(592,690)
(593,688)(594,689)(595,703)(596,704)(597,705)(598,711)(599,709)(600,710)
(601,707)(602,708)(603,706)(604,723)(605,721)(606,722)(607,728)(608,729)
(609,727)(610,724)(611,725)(612,726)(613,713)(614,714)(615,712)(616,718)
(617,719)(618,720)(619,717)(620,715)(621,716)(622,730)(623,731)(624,732)
(625,738)(626,736)(627,737)(628,734)(629,735)(630,733)(631,750)(632,748)
(633,749)(634,755)(635,756)(636,754)(637,751)(638,752)(639,753)(640,740)
(641,741)(642,739)(643,745)(644,746)(645,747)(646,744)(647,742)(648,743);;
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 := ( 1,217)( 2,219)( 3,218)( 4,238)( 5,240)( 6,239)( 7,234)( 8,233)
( 9,232)( 10,235)( 11,237)( 12,236)( 13,229)( 14,231)( 15,230)( 16,225)
( 17,224)( 18,223)( 19,226)( 20,228)( 21,227)( 22,220)( 23,222)( 24,221)
( 25,243)( 26,242)( 27,241)( 28,244)( 29,246)( 30,245)( 31,265)( 32,267)
( 33,266)( 34,261)( 35,260)( 36,259)( 37,262)( 38,264)( 39,263)( 40,256)
( 41,258)( 42,257)( 43,252)( 44,251)( 45,250)( 46,253)( 47,255)( 48,254)
( 49,247)( 50,249)( 51,248)( 52,270)( 53,269)( 54,268)( 55,298)( 56,300)
( 57,299)( 58,319)( 59,321)( 60,320)( 61,315)( 62,314)( 63,313)( 64,316)
( 65,318)( 66,317)( 67,310)( 68,312)( 69,311)( 70,306)( 71,305)( 72,304)
( 73,307)( 74,309)( 75,308)( 76,301)( 77,303)( 78,302)( 79,324)( 80,323)
( 81,322)( 82,271)( 83,273)( 84,272)( 85,292)( 86,294)( 87,293)( 88,288)
( 89,287)( 90,286)( 91,289)( 92,291)( 93,290)( 94,283)( 95,285)( 96,284)
( 97,279)( 98,278)( 99,277)(100,280)(101,282)(102,281)(103,274)(104,276)
(105,275)(106,297)(107,296)(108,295)(109,325)(110,327)(111,326)(112,346)
(113,348)(114,347)(115,342)(116,341)(117,340)(118,343)(119,345)(120,344)
(121,337)(122,339)(123,338)(124,333)(125,332)(126,331)(127,334)(128,336)
(129,335)(130,328)(131,330)(132,329)(133,351)(134,350)(135,349)(136,352)
(137,354)(138,353)(139,373)(140,375)(141,374)(142,369)(143,368)(144,367)
(145,370)(146,372)(147,371)(148,364)(149,366)(150,365)(151,360)(152,359)
(153,358)(154,361)(155,363)(156,362)(157,355)(158,357)(159,356)(160,378)
(161,377)(162,376)(163,406)(164,408)(165,407)(166,427)(167,429)(168,428)
(169,423)(170,422)(171,421)(172,424)(173,426)(174,425)(175,418)(176,420)
(177,419)(178,414)(179,413)(180,412)(181,415)(182,417)(183,416)(184,409)
(185,411)(186,410)(187,432)(188,431)(189,430)(190,379)(191,381)(192,380)
(193,400)(194,402)(195,401)(196,396)(197,395)(198,394)(199,397)(200,399)
(201,398)(202,391)(203,393)(204,392)(205,387)(206,386)(207,385)(208,388)
(209,390)(210,389)(211,382)(212,384)(213,383)(214,405)(215,404)(216,403)
(433,784)(434,786)(435,785)(436,805)(437,807)(438,806)(439,801)(440,800)
(441,799)(442,802)(443,804)(444,803)(445,796)(446,798)(447,797)(448,792)
(449,791)(450,790)(451,793)(452,795)(453,794)(454,787)(455,789)(456,788)
(457,810)(458,809)(459,808)(460,757)(461,759)(462,758)(463,778)(464,780)
(465,779)(466,774)(467,773)(468,772)(469,775)(470,777)(471,776)(472,769)
(473,771)(474,770)(475,765)(476,764)(477,763)(478,766)(479,768)(480,767)
(481,760)(482,762)(483,761)(484,783)(485,782)(486,781)(487,811)(488,813)
(489,812)(490,832)(491,834)(492,833)(493,828)(494,827)(495,826)(496,829)
(497,831)(498,830)(499,823)(500,825)(501,824)(502,819)(503,818)(504,817)
(505,820)(506,822)(507,821)(508,814)(509,816)(510,815)(511,837)(512,836)
(513,835)(514,838)(515,840)(516,839)(517,859)(518,861)(519,860)(520,855)
(521,854)(522,853)(523,856)(524,858)(525,857)(526,850)(527,852)(528,851)
(529,846)(530,845)(531,844)(532,847)(533,849)(534,848)(535,841)(536,843)
(537,842)(538,864)(539,863)(540,862)(541,649)(542,651)(543,650)(544,670)
(545,672)(546,671)(547,666)(548,665)(549,664)(550,667)(551,669)(552,668)
(553,661)(554,663)(555,662)(556,657)(557,656)(558,655)(559,658)(560,660)
(561,659)(562,652)(563,654)(564,653)(565,675)(566,674)(567,673)(568,676)
(569,678)(570,677)(571,697)(572,699)(573,698)(574,693)(575,692)(576,691)
(577,694)(578,696)(579,695)(580,688)(581,690)(582,689)(583,684)(584,683)
(585,682)(586,685)(587,687)(588,686)(589,679)(590,681)(591,680)(592,702)
(593,701)(594,700)(595,730)(596,732)(597,731)(598,751)(599,753)(600,752)
(601,747)(602,746)(603,745)(604,748)(605,750)(606,749)(607,742)(608,744)
(609,743)(610,738)(611,737)(612,736)(613,739)(614,741)(615,740)(616,733)
(617,735)(618,734)(619,756)(620,755)(621,754)(622,703)(623,705)(624,704)
(625,724)(626,726)(627,725)(628,720)(629,719)(630,718)(631,721)(632,723)
(633,722)(634,715)(635,717)(636,716)(637,711)(638,710)(639,709)(640,712)
(641,714)(642,713)(643,706)(644,708)(645,707)(646,729)(647,728)(648,727);;
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,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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,
s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0 ];;
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)(109,217)(110,218)(111,219)
(112,225)(113,223)(114,224)(115,221)(116,222)(117,220)(118,237)(119,235)
(120,236)(121,242)(122,243)(123,241)(124,238)(125,239)(126,240)(127,227)
(128,228)(129,226)(130,232)(131,233)(132,234)(133,231)(134,229)(135,230)
(136,244)(137,245)(138,246)(139,252)(140,250)(141,251)(142,248)(143,249)
(144,247)(145,264)(146,262)(147,263)(148,269)(149,270)(150,268)(151,265)
(152,266)(153,267)(154,254)(155,255)(156,253)(157,259)(158,260)(159,261)
(160,258)(161,256)(162,257)(163,271)(164,272)(165,273)(166,279)(167,277)
(168,278)(169,275)(170,276)(171,274)(172,291)(173,289)(174,290)(175,296)
(176,297)(177,295)(178,292)(179,293)(180,294)(181,281)(182,282)(183,280)
(184,286)(185,287)(186,288)(187,285)(188,283)(189,284)(190,298)(191,299)
(192,300)(193,306)(194,304)(195,305)(196,302)(197,303)(198,301)(199,318)
(200,316)(201,317)(202,323)(203,324)(204,322)(205,319)(206,320)(207,321)
(208,308)(209,309)(210,307)(211,313)(212,314)(213,315)(214,312)(215,310)
(216,311)(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)(541,649)(542,650)(543,651)
(544,657)(545,655)(546,656)(547,653)(548,654)(549,652)(550,669)(551,667)
(552,668)(553,674)(554,675)(555,673)(556,670)(557,671)(558,672)(559,659)
(560,660)(561,658)(562,664)(563,665)(564,666)(565,663)(566,661)(567,662)
(568,676)(569,677)(570,678)(571,684)(572,682)(573,683)(574,680)(575,681)
(576,679)(577,696)(578,694)(579,695)(580,701)(581,702)(582,700)(583,697)
(584,698)(585,699)(586,686)(587,687)(588,685)(589,691)(590,692)(591,693)
(592,690)(593,688)(594,689)(595,703)(596,704)(597,705)(598,711)(599,709)
(600,710)(601,707)(602,708)(603,706)(604,723)(605,721)(606,722)(607,728)
(608,729)(609,727)(610,724)(611,725)(612,726)(613,713)(614,714)(615,712)
(616,718)(617,719)(618,720)(619,717)(620,715)(621,716)(622,730)(623,731)
(624,732)(625,738)(626,736)(627,737)(628,734)(629,735)(630,733)(631,750)
(632,748)(633,749)(634,755)(635,756)(636,754)(637,751)(638,752)(639,753)
(640,740)(641,741)(642,739)(643,745)(644,746)(645,747)(646,744)(647,742)
(648,743);
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)!( 1,217)( 2,219)( 3,218)( 4,238)( 5,240)( 6,239)( 7,234)
( 8,233)( 9,232)( 10,235)( 11,237)( 12,236)( 13,229)( 14,231)( 15,230)
( 16,225)( 17,224)( 18,223)( 19,226)( 20,228)( 21,227)( 22,220)( 23,222)
( 24,221)( 25,243)( 26,242)( 27,241)( 28,244)( 29,246)( 30,245)( 31,265)
( 32,267)( 33,266)( 34,261)( 35,260)( 36,259)( 37,262)( 38,264)( 39,263)
( 40,256)( 41,258)( 42,257)( 43,252)( 44,251)( 45,250)( 46,253)( 47,255)
( 48,254)( 49,247)( 50,249)( 51,248)( 52,270)( 53,269)( 54,268)( 55,298)
( 56,300)( 57,299)( 58,319)( 59,321)( 60,320)( 61,315)( 62,314)( 63,313)
( 64,316)( 65,318)( 66,317)( 67,310)( 68,312)( 69,311)( 70,306)( 71,305)
( 72,304)( 73,307)( 74,309)( 75,308)( 76,301)( 77,303)( 78,302)( 79,324)
( 80,323)( 81,322)( 82,271)( 83,273)( 84,272)( 85,292)( 86,294)( 87,293)
( 88,288)( 89,287)( 90,286)( 91,289)( 92,291)( 93,290)( 94,283)( 95,285)
( 96,284)( 97,279)( 98,278)( 99,277)(100,280)(101,282)(102,281)(103,274)
(104,276)(105,275)(106,297)(107,296)(108,295)(109,325)(110,327)(111,326)
(112,346)(113,348)(114,347)(115,342)(116,341)(117,340)(118,343)(119,345)
(120,344)(121,337)(122,339)(123,338)(124,333)(125,332)(126,331)(127,334)
(128,336)(129,335)(130,328)(131,330)(132,329)(133,351)(134,350)(135,349)
(136,352)(137,354)(138,353)(139,373)(140,375)(141,374)(142,369)(143,368)
(144,367)(145,370)(146,372)(147,371)(148,364)(149,366)(150,365)(151,360)
(152,359)(153,358)(154,361)(155,363)(156,362)(157,355)(158,357)(159,356)
(160,378)(161,377)(162,376)(163,406)(164,408)(165,407)(166,427)(167,429)
(168,428)(169,423)(170,422)(171,421)(172,424)(173,426)(174,425)(175,418)
(176,420)(177,419)(178,414)(179,413)(180,412)(181,415)(182,417)(183,416)
(184,409)(185,411)(186,410)(187,432)(188,431)(189,430)(190,379)(191,381)
(192,380)(193,400)(194,402)(195,401)(196,396)(197,395)(198,394)(199,397)
(200,399)(201,398)(202,391)(203,393)(204,392)(205,387)(206,386)(207,385)
(208,388)(209,390)(210,389)(211,382)(212,384)(213,383)(214,405)(215,404)
(216,403)(433,784)(434,786)(435,785)(436,805)(437,807)(438,806)(439,801)
(440,800)(441,799)(442,802)(443,804)(444,803)(445,796)(446,798)(447,797)
(448,792)(449,791)(450,790)(451,793)(452,795)(453,794)(454,787)(455,789)
(456,788)(457,810)(458,809)(459,808)(460,757)(461,759)(462,758)(463,778)
(464,780)(465,779)(466,774)(467,773)(468,772)(469,775)(470,777)(471,776)
(472,769)(473,771)(474,770)(475,765)(476,764)(477,763)(478,766)(479,768)
(480,767)(481,760)(482,762)(483,761)(484,783)(485,782)(486,781)(487,811)
(488,813)(489,812)(490,832)(491,834)(492,833)(493,828)(494,827)(495,826)
(496,829)(497,831)(498,830)(499,823)(500,825)(501,824)(502,819)(503,818)
(504,817)(505,820)(506,822)(507,821)(508,814)(509,816)(510,815)(511,837)
(512,836)(513,835)(514,838)(515,840)(516,839)(517,859)(518,861)(519,860)
(520,855)(521,854)(522,853)(523,856)(524,858)(525,857)(526,850)(527,852)
(528,851)(529,846)(530,845)(531,844)(532,847)(533,849)(534,848)(535,841)
(536,843)(537,842)(538,864)(539,863)(540,862)(541,649)(542,651)(543,650)
(544,670)(545,672)(546,671)(547,666)(548,665)(549,664)(550,667)(551,669)
(552,668)(553,661)(554,663)(555,662)(556,657)(557,656)(558,655)(559,658)
(560,660)(561,659)(562,652)(563,654)(564,653)(565,675)(566,674)(567,673)
(568,676)(569,678)(570,677)(571,697)(572,699)(573,698)(574,693)(575,692)
(576,691)(577,694)(578,696)(579,695)(580,688)(581,690)(582,689)(583,684)
(584,683)(585,682)(586,685)(587,687)(588,686)(589,679)(590,681)(591,680)
(592,702)(593,701)(594,700)(595,730)(596,732)(597,731)(598,751)(599,753)
(600,752)(601,747)(602,746)(603,745)(604,748)(605,750)(606,749)(607,742)
(608,744)(609,743)(610,738)(611,737)(612,736)(613,739)(614,741)(615,740)
(616,733)(617,735)(618,734)(619,756)(620,755)(621,754)(622,703)(623,705)
(624,704)(625,724)(626,726)(627,725)(628,720)(629,719)(630,718)(631,721)
(632,723)(633,722)(634,715)(635,717)(636,716)(637,711)(638,710)(639,709)
(640,712)(641,714)(642,713)(643,706)(644,708)(645,707)(646,729)(647,728)
(648,727);
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,
s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1,
s0*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*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,
s1*s2*s1*s0*s1*s0*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s0 >;
References : None.
to this polytope