Polytope of Type {12,24}
This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,24}*1728s
if this polytope has a name.
Group : SmallGroup(1728,31593)
Rank : 3
Schlafli Type : {12,24}
Number of vertices, edges, etc : 36, 432, 72
Order of s0s1s2 : 8
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 : {12,12}*864j, {6,24}*864g
3-fold quotients : {12,8}*576a
4-fold quotients : {6,12}*432h
6-fold quotients : {6,8}*288, {12,4}*288
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)( 2,327)( 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)(109,244)(110,246)(111,245)(112,250)
(113,252)(114,251)(115,247)(116,249)(117,248)(118,262)(119,264)(120,263)
(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,253)(128,255)
(129,254)(130,259)(131,261)(132,260)(133,256)(134,258)(135,257)(136,217)
(137,219)(138,218)(139,223)(140,225)(141,224)(142,220)(143,222)(144,221)
(145,235)(146,237)(147,236)(148,241)(149,243)(150,242)(151,238)(152,240)
(153,239)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)(160,229)
(161,231)(162,230)(163,298)(164,300)(165,299)(166,304)(167,306)(168,305)
(169,301)(170,303)(171,302)(172,316)(173,318)(174,317)(175,322)(176,324)
(177,323)(178,319)(179,321)(180,320)(181,307)(182,309)(183,308)(184,313)
(185,315)(186,314)(187,310)(188,312)(189,311)(190,271)(191,273)(192,272)
(193,277)(194,279)(195,278)(196,274)(197,276)(198,275)(199,289)(200,291)
(201,290)(202,295)(203,297)(204,296)(205,292)(206,294)(207,293)(208,280)
(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)(216,284)
(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)(541,676)(542,678)(543,677)(544,682)
(545,684)(546,683)(547,679)(548,681)(549,680)(550,694)(551,696)(552,695)
(553,700)(554,702)(555,701)(556,697)(557,699)(558,698)(559,685)(560,687)
(561,686)(562,691)(563,693)(564,692)(565,688)(566,690)(567,689)(568,649)
(569,651)(570,650)(571,655)(572,657)(573,656)(574,652)(575,654)(576,653)
(577,667)(578,669)(579,668)(580,673)(581,675)(582,674)(583,670)(584,672)
(585,671)(586,658)(587,660)(588,659)(589,664)(590,666)(591,665)(592,661)
(593,663)(594,662)(595,730)(596,732)(597,731)(598,736)(599,738)(600,737)
(601,733)(602,735)(603,734)(604,748)(605,750)(606,749)(607,754)(608,756)
(609,755)(610,751)(611,753)(612,752)(613,739)(614,741)(615,740)(616,745)
(617,747)(618,746)(619,742)(620,744)(621,743)(622,703)(623,705)(624,704)
(625,709)(626,711)(627,710)(628,706)(629,708)(630,707)(631,721)(632,723)
(633,722)(634,727)(635,729)(636,728)(637,724)(638,726)(639,725)(640,712)
(641,714)(642,713)(643,718)(644,720)(645,719)(646,715)(647,717)(648,716);;
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 := ( 1,217)( 2,224)( 3,222)( 4,223)( 5,221)( 6,219)( 7,220)( 8,218)
( 9,225)( 10,235)( 11,242)( 12,240)( 13,241)( 14,239)( 15,237)( 16,238)
( 17,236)( 18,243)( 19,226)( 20,233)( 21,231)( 22,232)( 23,230)( 24,228)
( 25,229)( 26,227)( 27,234)( 28,244)( 29,251)( 30,249)( 31,250)( 32,248)
( 33,246)( 34,247)( 35,245)( 36,252)( 37,262)( 38,269)( 39,267)( 40,268)
( 41,266)( 42,264)( 43,265)( 44,263)( 45,270)( 46,253)( 47,260)( 48,258)
( 49,259)( 50,257)( 51,255)( 52,256)( 53,254)( 54,261)( 55,271)( 56,278)
( 57,276)( 58,277)( 59,275)( 60,273)( 61,274)( 62,272)( 63,279)( 64,289)
( 65,296)( 66,294)( 67,295)( 68,293)( 69,291)( 70,292)( 71,290)( 72,297)
( 73,280)( 74,287)( 75,285)( 76,286)( 77,284)( 78,282)( 79,283)( 80,281)
( 81,288)( 82,298)( 83,305)( 84,303)( 85,304)( 86,302)( 87,300)( 88,301)
( 89,299)( 90,306)( 91,316)( 92,323)( 93,321)( 94,322)( 95,320)( 96,318)
( 97,319)( 98,317)( 99,324)(100,307)(101,314)(102,312)(103,313)(104,311)
(105,309)(106,310)(107,308)(108,315)(109,352)(110,359)(111,357)(112,358)
(113,356)(114,354)(115,355)(116,353)(117,360)(118,370)(119,377)(120,375)
(121,376)(122,374)(123,372)(124,373)(125,371)(126,378)(127,361)(128,368)
(129,366)(130,367)(131,365)(132,363)(133,364)(134,362)(135,369)(136,325)
(137,332)(138,330)(139,331)(140,329)(141,327)(142,328)(143,326)(144,333)
(145,343)(146,350)(147,348)(148,349)(149,347)(150,345)(151,346)(152,344)
(153,351)(154,334)(155,341)(156,339)(157,340)(158,338)(159,336)(160,337)
(161,335)(162,342)(163,406)(164,413)(165,411)(166,412)(167,410)(168,408)
(169,409)(170,407)(171,414)(172,424)(173,431)(174,429)(175,430)(176,428)
(177,426)(178,427)(179,425)(180,432)(181,415)(182,422)(183,420)(184,421)
(185,419)(186,417)(187,418)(188,416)(189,423)(190,379)(191,386)(192,384)
(193,385)(194,383)(195,381)(196,382)(197,380)(198,387)(199,397)(200,404)
(201,402)(202,403)(203,401)(204,399)(205,400)(206,398)(207,405)(208,388)
(209,395)(210,393)(211,394)(212,392)(213,390)(214,391)(215,389)(216,396)
(433,757)(434,764)(435,762)(436,763)(437,761)(438,759)(439,760)(440,758)
(441,765)(442,775)(443,782)(444,780)(445,781)(446,779)(447,777)(448,778)
(449,776)(450,783)(451,766)(452,773)(453,771)(454,772)(455,770)(456,768)
(457,769)(458,767)(459,774)(460,784)(461,791)(462,789)(463,790)(464,788)
(465,786)(466,787)(467,785)(468,792)(469,802)(470,809)(471,807)(472,808)
(473,806)(474,804)(475,805)(476,803)(477,810)(478,793)(479,800)(480,798)
(481,799)(482,797)(483,795)(484,796)(485,794)(486,801)(487,811)(488,818)
(489,816)(490,817)(491,815)(492,813)(493,814)(494,812)(495,819)(496,829)
(497,836)(498,834)(499,835)(500,833)(501,831)(502,832)(503,830)(504,837)
(505,820)(506,827)(507,825)(508,826)(509,824)(510,822)(511,823)(512,821)
(513,828)(514,838)(515,845)(516,843)(517,844)(518,842)(519,840)(520,841)
(521,839)(522,846)(523,856)(524,863)(525,861)(526,862)(527,860)(528,858)
(529,859)(530,857)(531,864)(532,847)(533,854)(534,852)(535,853)(536,851)
(537,849)(538,850)(539,848)(540,855)(541,649)(542,656)(543,654)(544,655)
(545,653)(546,651)(547,652)(548,650)(549,657)(550,667)(551,674)(552,672)
(553,673)(554,671)(555,669)(556,670)(557,668)(558,675)(559,658)(560,665)
(561,663)(562,664)(563,662)(564,660)(565,661)(566,659)(567,666)(568,676)
(569,683)(570,681)(571,682)(572,680)(573,678)(574,679)(575,677)(576,684)
(577,694)(578,701)(579,699)(580,700)(581,698)(582,696)(583,697)(584,695)
(585,702)(586,685)(587,692)(588,690)(589,691)(590,689)(591,687)(592,688)
(593,686)(594,693)(595,703)(596,710)(597,708)(598,709)(599,707)(600,705)
(601,706)(602,704)(603,711)(604,721)(605,728)(606,726)(607,727)(608,725)
(609,723)(610,724)(611,722)(612,729)(613,712)(614,719)(615,717)(616,718)
(617,716)(618,714)(619,715)(620,713)(621,720)(622,730)(623,737)(624,735)
(625,736)(626,734)(627,732)(628,733)(629,731)(630,738)(631,748)(632,755)
(633,753)(634,754)(635,752)(636,750)(637,751)(638,749)(639,756)(640,739)
(641,746)(642,744)(643,745)(644,743)(645,741)(646,742)(647,740)(648,747);;
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*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*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*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)( 2,327)( 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)(109,244)(110,246)(111,245)
(112,250)(113,252)(114,251)(115,247)(116,249)(117,248)(118,262)(119,264)
(120,263)(121,268)(122,270)(123,269)(124,265)(125,267)(126,266)(127,253)
(128,255)(129,254)(130,259)(131,261)(132,260)(133,256)(134,258)(135,257)
(136,217)(137,219)(138,218)(139,223)(140,225)(141,224)(142,220)(143,222)
(144,221)(145,235)(146,237)(147,236)(148,241)(149,243)(150,242)(151,238)
(152,240)(153,239)(154,226)(155,228)(156,227)(157,232)(158,234)(159,233)
(160,229)(161,231)(162,230)(163,298)(164,300)(165,299)(166,304)(167,306)
(168,305)(169,301)(170,303)(171,302)(172,316)(173,318)(174,317)(175,322)
(176,324)(177,323)(178,319)(179,321)(180,320)(181,307)(182,309)(183,308)
(184,313)(185,315)(186,314)(187,310)(188,312)(189,311)(190,271)(191,273)
(192,272)(193,277)(194,279)(195,278)(196,274)(197,276)(198,275)(199,289)
(200,291)(201,290)(202,295)(203,297)(204,296)(205,292)(206,294)(207,293)
(208,280)(209,282)(210,281)(211,286)(212,288)(213,287)(214,283)(215,285)
(216,284)(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)(541,676)(542,678)(543,677)
(544,682)(545,684)(546,683)(547,679)(548,681)(549,680)(550,694)(551,696)
(552,695)(553,700)(554,702)(555,701)(556,697)(557,699)(558,698)(559,685)
(560,687)(561,686)(562,691)(563,693)(564,692)(565,688)(566,690)(567,689)
(568,649)(569,651)(570,650)(571,655)(572,657)(573,656)(574,652)(575,654)
(576,653)(577,667)(578,669)(579,668)(580,673)(581,675)(582,674)(583,670)
(584,672)(585,671)(586,658)(587,660)(588,659)(589,664)(590,666)(591,665)
(592,661)(593,663)(594,662)(595,730)(596,732)(597,731)(598,736)(599,738)
(600,737)(601,733)(602,735)(603,734)(604,748)(605,750)(606,749)(607,754)
(608,756)(609,755)(610,751)(611,753)(612,752)(613,739)(614,741)(615,740)
(616,745)(617,747)(618,746)(619,742)(620,744)(621,743)(622,703)(623,705)
(624,704)(625,709)(626,711)(627,710)(628,706)(629,708)(630,707)(631,721)
(632,723)(633,722)(634,727)(635,729)(636,728)(637,724)(638,726)(639,725)
(640,712)(641,714)(642,713)(643,718)(644,720)(645,719)(646,715)(647,717)
(648,716);
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)!( 1,217)( 2,224)( 3,222)( 4,223)( 5,221)( 6,219)( 7,220)
( 8,218)( 9,225)( 10,235)( 11,242)( 12,240)( 13,241)( 14,239)( 15,237)
( 16,238)( 17,236)( 18,243)( 19,226)( 20,233)( 21,231)( 22,232)( 23,230)
( 24,228)( 25,229)( 26,227)( 27,234)( 28,244)( 29,251)( 30,249)( 31,250)
( 32,248)( 33,246)( 34,247)( 35,245)( 36,252)( 37,262)( 38,269)( 39,267)
( 40,268)( 41,266)( 42,264)( 43,265)( 44,263)( 45,270)( 46,253)( 47,260)
( 48,258)( 49,259)( 50,257)( 51,255)( 52,256)( 53,254)( 54,261)( 55,271)
( 56,278)( 57,276)( 58,277)( 59,275)( 60,273)( 61,274)( 62,272)( 63,279)
( 64,289)( 65,296)( 66,294)( 67,295)( 68,293)( 69,291)( 70,292)( 71,290)
( 72,297)( 73,280)( 74,287)( 75,285)( 76,286)( 77,284)( 78,282)( 79,283)
( 80,281)( 81,288)( 82,298)( 83,305)( 84,303)( 85,304)( 86,302)( 87,300)
( 88,301)( 89,299)( 90,306)( 91,316)( 92,323)( 93,321)( 94,322)( 95,320)
( 96,318)( 97,319)( 98,317)( 99,324)(100,307)(101,314)(102,312)(103,313)
(104,311)(105,309)(106,310)(107,308)(108,315)(109,352)(110,359)(111,357)
(112,358)(113,356)(114,354)(115,355)(116,353)(117,360)(118,370)(119,377)
(120,375)(121,376)(122,374)(123,372)(124,373)(125,371)(126,378)(127,361)
(128,368)(129,366)(130,367)(131,365)(132,363)(133,364)(134,362)(135,369)
(136,325)(137,332)(138,330)(139,331)(140,329)(141,327)(142,328)(143,326)
(144,333)(145,343)(146,350)(147,348)(148,349)(149,347)(150,345)(151,346)
(152,344)(153,351)(154,334)(155,341)(156,339)(157,340)(158,338)(159,336)
(160,337)(161,335)(162,342)(163,406)(164,413)(165,411)(166,412)(167,410)
(168,408)(169,409)(170,407)(171,414)(172,424)(173,431)(174,429)(175,430)
(176,428)(177,426)(178,427)(179,425)(180,432)(181,415)(182,422)(183,420)
(184,421)(185,419)(186,417)(187,418)(188,416)(189,423)(190,379)(191,386)
(192,384)(193,385)(194,383)(195,381)(196,382)(197,380)(198,387)(199,397)
(200,404)(201,402)(202,403)(203,401)(204,399)(205,400)(206,398)(207,405)
(208,388)(209,395)(210,393)(211,394)(212,392)(213,390)(214,391)(215,389)
(216,396)(433,757)(434,764)(435,762)(436,763)(437,761)(438,759)(439,760)
(440,758)(441,765)(442,775)(443,782)(444,780)(445,781)(446,779)(447,777)
(448,778)(449,776)(450,783)(451,766)(452,773)(453,771)(454,772)(455,770)
(456,768)(457,769)(458,767)(459,774)(460,784)(461,791)(462,789)(463,790)
(464,788)(465,786)(466,787)(467,785)(468,792)(469,802)(470,809)(471,807)
(472,808)(473,806)(474,804)(475,805)(476,803)(477,810)(478,793)(479,800)
(480,798)(481,799)(482,797)(483,795)(484,796)(485,794)(486,801)(487,811)
(488,818)(489,816)(490,817)(491,815)(492,813)(493,814)(494,812)(495,819)
(496,829)(497,836)(498,834)(499,835)(500,833)(501,831)(502,832)(503,830)
(504,837)(505,820)(506,827)(507,825)(508,826)(509,824)(510,822)(511,823)
(512,821)(513,828)(514,838)(515,845)(516,843)(517,844)(518,842)(519,840)
(520,841)(521,839)(522,846)(523,856)(524,863)(525,861)(526,862)(527,860)
(528,858)(529,859)(530,857)(531,864)(532,847)(533,854)(534,852)(535,853)
(536,851)(537,849)(538,850)(539,848)(540,855)(541,649)(542,656)(543,654)
(544,655)(545,653)(546,651)(547,652)(548,650)(549,657)(550,667)(551,674)
(552,672)(553,673)(554,671)(555,669)(556,670)(557,668)(558,675)(559,658)
(560,665)(561,663)(562,664)(563,662)(564,660)(565,661)(566,659)(567,666)
(568,676)(569,683)(570,681)(571,682)(572,680)(573,678)(574,679)(575,677)
(576,684)(577,694)(578,701)(579,699)(580,700)(581,698)(582,696)(583,697)
(584,695)(585,702)(586,685)(587,692)(588,690)(589,691)(590,689)(591,687)
(592,688)(593,686)(594,693)(595,703)(596,710)(597,708)(598,709)(599,707)
(600,705)(601,706)(602,704)(603,711)(604,721)(605,728)(606,726)(607,727)
(608,725)(609,723)(610,724)(611,722)(612,729)(613,712)(614,719)(615,717)
(616,718)(617,716)(618,714)(619,715)(620,713)(621,720)(622,730)(623,737)
(624,735)(625,736)(626,734)(627,732)(628,733)(629,731)(630,738)(631,748)
(632,755)(633,753)(634,754)(635,752)(636,750)(637,751)(638,749)(639,756)
(640,739)(641,746)(642,744)(643,745)(644,743)(645,741)(646,742)(647,740)
(648,747);
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*s0*s1*s2*s1*s0*s1*s2*s0*s1*s0*s1*s2*s1*s0*s1,
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1,
s2*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2*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*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