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Polytope of Type {12,24}

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