Polytope of Type {9,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,12}*1944c
if this polytope has a name.
Group : SmallGroup(1944,3453)
Rank : 3
Schlafli Type : {9,12}
Number of vertices, edges, etc : 81, 486, 108
Order of s₀s₁s₂ : 9
Order of s₀s₁s₂s₁ : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {9,12}*648b
   27-fold quotients : {9,4}*72
   81-fold quotients : {3,4}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 3.
      36 facets:
         36 of {9}*18
      45 vertex figures:
         18 of {12}*24
         27 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 3.
      36 facets:
         36 of {9}*18
      27 vertex figures:
         27 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 3.
      36 facets:
         36 of {9}*18
      27 vertex figures:
         27 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1> of order 3.
      54 facets:
         27 of {3}*6
         27 of {9}*18
      27 vertex figures:
         27 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s2> of order 3.
      36 facets:
         36 of {9}*18
      27 vertex figures:
         27 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1, s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 9.
      24 facets:
         18 of {3}*6
         6 of {9}*18
      9 vertex figures:
         9 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2, s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 9.
      12 facets:
         12 of {9}*18
      21 vertex figures:
         3 of {12}*24
         18 of {4}*8
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s1*s2, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1> of order 9.
      12 facets:
         12 of {9}*18
      9 vertex figures:
         9 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 9.
      12 facets:
         12 of {9}*18
      15 vertex figures:
         6 of {12}*24
         9 of {4}*8

Permutation Representation (GAP) :

s0 := (  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 10)(  8, 12)(  9, 11)( 13, 25)( 14, 27)( 15, 26)( 17, 18)( 23, 24)( 28, 55)( 29, 57)( 30, 56)( 31, 73)( 32, 75)( 33, 74)( 34, 64)( 35, 66)
( 36, 65)( 37, 61)( 38, 63)( 39, 62)( 40, 79)( 41, 81)( 42, 80)( 43, 70)( 44, 72)( 45, 71)( 46, 58)( 47, 60)( 48, 59)( 49, 76)( 50, 78)( 51, 77)( 52, 67)( 53, 69)( 54, 68)( 83, 84)( 85,100)( 86,102)( 87,101)( 88, 91)( 89, 93)( 90, 92)( 94,106)( 95,108)( 96,107)( 98, 99)(104,105)(109,217)(110,219)(111,218)(112,235)(113,237)(114,236)(115,226)(116,228)(117,227)(118,223)(119,225)(120,224)(121,241)(122,243)(123,242)(124,232)(125,234)(126,233)(127,220)(128,222)(129,221)(130,238)(131,240)(132,239)(133,229)(134,231)(135,230)(136,271)(137,273)(138,272)(139,289)(140,291)(141,290)(142,280)(143,282)(144,281)(145,277)(146,279)(147,278)(148,295)(149,297)(150,296)(151,286)(152,288)(153,287)(154,274)(155,276)(156,275)(157,292)(158,294)(159,293)(160,283)(161,285)(162,284)(163,244)(164,246)(165,245)(166,262)(167,264)(168,263)(169,253)(170,255)(171,254)(172,250)(173,252)(174,251)(175,268)(176,270)(177,269)(178,259)(179,261)(180,260)(181,247)(182,249)(183,248)(184,265)(185,267)(186,266)(187,256)(188,258)(189,257)(190,298)(191,300)(192,299)(193,316)(194,318)(195,317)(196,307)(197,309)(198,308)(199,304)(200,306)(201,305)(202,322)(203,324)(204,323)(205,313)(206,315)(207,314)(208,301)(209,303)(210,302)(211,319)(212,321)(213,320)(214,310)(215,312)(216,311)(325,865)(326,867)(327,866)(328,883)(329,885)(330,884)(331,874)(332,876)(333,875)(334,871)(335,873)(336,872)(337,889)(338,891)(339,890)(340,880)(341,882)(342,881)(343,868)(344,870)(345,869)(346,886)(347,888)(348,887)(349,877)(350,879)(351,878)(352,919)(353,921)(354,920)(355,937)(356,939)(357,938)(358,928)(359,930)(360,929)(361,925)(362,927)(363,926)(364,943)(365,945)(366,944)(367,934)(368,936)(369,935)(370,922)(371,924)(372,923)(373,940)(374,942)(375,941)(376,931)(377,933)(378,932)(379,892)(380,894)(381,893)(382,910)(383,912)(384,911)(385,901)(386,903)(387,902)(388,898)(389,900)(390,899)(391,916)(392,918)(393,917)(394,907)(395,909)(396,908)(397,895)(398,897)(399,896)(400,913)(401,915)(402,914)(403,904)(404,906)(405,905)(406,946)(407,948)(408,947)(409,964)(410,966)(411,965)(412,955)(413,957)(414,956)(415,952)(416,954)(417,953)(418,970)(419,972)(420,971)(421,961)(422,963)(423,962)(424,949)(425,951)(426,950)(427,967)(428,969)(429,968)(430,958)(431,960)(432,959)(433,757)(434,759)(435,758)(436,775)(437,777)(438,776)(439,766)(440,768)(441,767)(442,763)(443,765)(444,764)(445,781)(446,783)(447,782)(448,772)(449,774)(450,773)(451,760)(452,762)(453,761)(454,778)(455,780)(456,779)(457,769)(458,771)(459,770)(460,811)(461,813)(462,812)(463,829)(464,831)(465,830)(466,820)(467,822)(468,821)(469,817)(470,819)(471,818)(472,835)(473,837)(474,836)(475,826)(476,828)(477,827)(478,814)(479,816)(480,815)(481,832)(482,834)(483,833)(484,823)(485,825)(486,824)(487,784)(488,786)(489,785)(490,802)(491,804)(492,803)(493,793)(494,795)(495,794)(496,790)(497,792)(498,791)(499,808)(500,810)(501,809)(502,799)(503,801)(504,800)(505,787)(506,789)(507,788)(508,805)(509,807)(510,806)(511,796)(512,798)(513,797)(514,838)(515,840)(516,839)(517,856)(518,858)(519,857)(520,847)(521,849)(522,848)(523,844)(524,846)(525,845)(526,862)(527,864)(528,863)(529,853)(530,855)(531,854)(532,841)(533,843)(534,842)(535,859)(536,861)(537,860)(538,850)(539,852)(540,851)(541,649)(542,651)(543,650)(544,667)(545,669)(546,668)(547,658)(548,660)(549,659)(550,655)(551,657)(552,656)(553,673)(554,675)(555,674)(556,664)(557,666)(558,665)(559,652)(560,654)(561,653)(562,670)(563,672)(564,671)(565,661)(566,663)(567,662)(568,703)(569,705)(570,704)(571,721)(572,723)(573,722)(574,712)(575,714)(576,713)(577,709)(578,711)(579,710)(580,727)(581,729)(582,728)(583,718)(584,720)(585,719)(586,706)(587,708)(588,707)(589,724)(590,726)(591,725)(592,715)(593,717)(594,716)(595,676)(596,678)(597,677)(598,694)(599,696)(600,695)(601,685)(602,687)(603,686)(604,682)(605,684)(606,683)(607,700)(608,702)(609,701)(610,691)(611,693)(612,692)(613,679)(614,681)(615,680)(616,697)(617,699)(618,698)(619,688)(620,690)(621,689)(622,730)(623,732)(624,731)(625,748)(626,750)(627,749)(628,739)(629,741)(630,740)(631,736)(632,738)(633,737)(634,754)(635,756)(636,755)(637,745)(638,747)(639,746)
(640,733)(641,735)(642,734)(643,751)(644,753)(645,752)(646,742)(647,744)(648,743);;
s1 := (  1,334)(  2,340)(  3,337)(  4,336)(  5,342)(  6,339)(  7,335)(  8,341)(  9,338)( 10,325)( 11,331)( 12,328)( 13,327)( 14,333)( 15,330)( 16,326)( 17,332)( 18,329)( 19,343)( 20,349)
( 21,346)( 22,345)( 23,351)( 24,348)( 25,344)( 26,350)( 27,347)( 28,361)( 29,367)( 30,364)( 31,363)( 32,369)( 33,366)( 34,362)( 35,368)( 36,365)( 37,352)( 38,358)( 39,355)( 40,354)( 41,360)( 42,357)( 43,353)( 44,359)( 45,356)( 46,370)( 47,376)( 48,373)( 49,372)( 50,378)( 51,375)( 52,371)( 53,377)( 54,374)( 55,415)( 56,421)( 57,418)( 58,417)( 59,423)( 60,420)( 61,416)( 62,422)( 63,419)( 64,406)( 65,412)( 66,409)( 67,408)( 68,414)( 69,411)( 70,407)( 71,413)( 72,410)( 73,424)( 74,430)( 75,427)( 76,426)( 77,432)( 78,429)( 79,425)( 80,431)( 81,428)( 82,388)( 83,394)( 84,391)( 85,390)( 86,396)( 87,393)( 88,389)( 89,395)( 90,392)( 91,379)( 92,385)( 93,382)( 94,381)( 95,387)( 96,384)( 97,380)( 98,386)( 99,383)(100,397)(101,403)(102,400)(103,399)(104,405)(105,402)(106,398)(107,404)(108,401)(109,550)(110,556)(111,553)(112,552)(113,558)(114,555)(115,551)(116,557)(117,554)(118,541)(119,547)(120,544)(121,543)(122,549)(123,546)(124,542)(125,548)(126,545)(127,559)(128,565)(129,562)(130,561)(131,567)(132,564)(133,560)(134,566)(135,563)(136,577)(137,583)(138,580)(139,579)(140,585)(141,582)(142,578)(143,584)(144,581)(145,568)(146,574)(147,571)(148,570)(149,576)(150,573)(151,569)(152,575)(153,572)(154,586)(155,592)(156,589)(157,588)(158,594)(159,591)(160,587)(161,593)(162,590)(163,631)(164,637)(165,634)(166,633)(167,639)(168,636)(169,632)(170,638)(171,635)(172,622)(173,628)(174,625)(175,624)(176,630)(177,627)(178,623)(179,629)(180,626)(181,640)(182,646)(183,643)(184,642)(185,648)(186,645)(187,641)(188,647)(189,644)(190,604)(191,610)(192,607)(193,606)(194,612)(195,609)(196,605)(197,611)(198,608)(199,595)(200,601)(201,598)(202,597)(203,603)(204,600)(205,596)(206,602)(207,599)(208,613)(209,619)(210,616)(211,615)(212,621)(213,618)(214,614)(215,620)(216,617)(217,442)(218,448)(219,445)(220,444)(221,450)(222,447)(223,443)(224,449)(225,446)(226,433)(227,439)(228,436)(229,435)(230,441)(231,438)(232,434)(233,440)(234,437)(235,451)(236,457)(237,454)(238,453)(239,459)(240,456)(241,452)(242,458)(243,455)(244,469)(245,475)(246,472)(247,471)(248,477)(249,474)(250,470)(251,476)(252,473)(253,460)(254,466)(255,463)(256,462)(257,468)(258,465)(259,461)(260,467)(261,464)(262,478)(263,484)(264,481)(265,480)(266,486)(267,483)(268,479)(269,485)(270,482)(271,523)(272,529)(273,526)(274,525)(275,531)(276,528)(277,524)(278,530)(279,527)(280,514)(281,520)(282,517)(283,516)(284,522)(285,519)(286,515)(287,521)(288,518)(289,532)(290,538)(291,535)(292,534)(293,540)(294,537)(295,533)(296,539)(297,536)(298,496)(299,502)(300,499)(301,498)(302,504)(303,501)(304,497)(305,503)(306,500)(307,487)(308,493)(309,490)(310,489)(311,495)(312,492)(313,488)(314,494)(315,491)(316,505)(317,511)(318,508)(319,507)(320,513)(321,510)(322,506)(323,512)(324,509)(649,874)(650,880)(651,877)(652,876)(653,882)(654,879)(655,875)(656,881)(657,878)(658,865)(659,871)(660,868)(661,867)(662,873)(663,870)(664,866)(665,872)(666,869)(667,883)(668,889)(669,886)(670,885)(671,891)(672,888)(673,884)(674,890)(675,887)(676,901)(677,907)(678,904)(679,903)(680,909)(681,906)(682,902)(683,908)(684,905)(685,892)(686,898)(687,895)(688,894)(689,900)(690,897)(691,893)(692,899)(693,896)(694,910)(695,916)(696,913)(697,912)(698,918)(699,915)(700,911)(701,917)(702,914)(703,955)(704,961)(705,958)(706,957)(707,963)(708,960)(709,956)(710,962)(711,959)(712,946)(713,952)(714,949)(715,948)(716,954)(717,951)(718,947)(719,953)(720,950)(721,964)(722,970)(723,967)(724,966)(725,972)(726,969)(727,965)(728,971)(729,968)(730,928)(731,934)(732,931)(733,930)(734,936)(735,933)(736,929)(737,935)(738,932)(739,919)(740,925)(741,922)(742,921)(743,927)(744,924)(745,920)(746,926)(747,923)(748,937)(749,943)(750,940)(751,939)(752,945)(753,942)(754,938)(755,944)(756,941)(757,766)(758,772)(759,769)(760,768)(761,774)(762,771)(763,767)(764,773)(765,770)(776,781)(777,778)(779,783)(784,793)(785,799)(786,796)(787,795)(788,801)(789,798)(790,794)(791,800)(792,797)(803,808)(804,805)(806,810)(811,847)(812,853)(813,850)(814,849)(815,855)(816,852)(817,848)(818,854)(819,851)(820,838)(821,844)(822,841)(823,840)(824,846)(825,843)(826,839)(827,845)(828,842)
(829,856)(830,862)(831,859)(832,858)(833,864)(834,861)(835,857)(836,863)(837,860);;
s2 := (  1,103)(  2,104)(  3,105)(  4,100)(  5,101)(  6,102)(  7,106)(  8,107)(  9,108)( 10, 94)( 11, 95)( 12, 96)( 13, 91)( 14, 92)( 15, 93)( 16, 97)( 17, 98)( 18, 99)( 19, 85)( 20, 86)
( 21, 87)( 22, 82)( 23, 83)( 24, 84)( 25, 88)( 26, 89)( 27, 90)( 28, 76)( 29, 77)( 30, 78)( 31, 73)( 32, 74)( 33, 75)( 34, 79)( 35, 80)( 36, 81)( 37, 67)( 38, 68)( 39, 69)( 40, 64)( 41, 65)( 42, 66)( 43, 70)( 44, 71)( 45, 72)( 46, 58)( 47, 59)( 48, 60)( 49, 55)( 50, 56)( 51, 57)( 52, 61)( 53, 62)( 54, 63)(109,211)(110,212)(111,213)(112,208)(113,209)(114,210)(115,214)(116,215)(117,216)(118,202)(119,203)(120,204)(121,199)(122,200)(123,201)(124,205)(125,206)(126,207)(127,193)(128,194)(129,195)(130,190)(131,191)(132,192)(133,196)(134,197)(135,198)(136,184)(137,185)(138,186)(139,181)(140,182)(141,183)(142,187)(143,188)(144,189)(145,175)(146,176)(147,177)(148,172)(149,173)(150,174)(151,178)(152,179)(153,180)(154,166)(155,167)(156,168)(157,163)(158,164)(159,165)(160,169)(161,170)(162,171)(217,319)(218,320)(219,321)(220,316)(221,317)(222,318)(223,322)(224,323)(225,324)(226,310)(227,311)(228,312)(229,307)(230,308)(231,309)(232,313)(233,314)(234,315)(235,301)(236,302)(237,303)(238,298)(239,299)(240,300)(241,304)(242,305)(243,306)(244,292)(245,293)(246,294)(247,289)(248,290)(249,291)(250,295)(251,296)(252,297)(253,283)(254,284)(255,285)(256,280)(257,281)(258,282)(259,286)(260,287)(261,288)(262,274)(263,275)(264,276)(265,271)(266,272)(267,273)(268,277)(269,278)(270,279)(325,427)(326,428)(327,429)(328,424)(329,425)(330,426)(331,430)(332,431)(333,432)(334,418)(335,419)(336,420)(337,415)(338,416)(339,417)(340,421)(341,422)(342,423)(343,409)(344,410)(345,411)(346,406)(347,407)(348,408)(349,412)(350,413)(351,414)(352,400)(353,401)(354,402)(355,397)(356,398)(357,399)(358,403)(359,404)(360,405)(361,391)(362,392)(363,393)(364,388)(365,389)(366,390)(367,394)(368,395)(369,396)(370,382)(371,383)(372,384)(373,379)(374,380)(375,381)(376,385)(377,386)(378,387)(433,535)(434,536)(435,537)(436,532)(437,533)(438,534)(439,538)(440,539)(441,540)(442,526)(443,527)(444,528)(445,523)(446,524)(447,525)(448,529)(449,530)(450,531)(451,517)(452,518)(453,519)(454,514)(455,515)(456,516)(457,520)(458,521)(459,522)(460,508)(461,509)(462,510)(463,505)(464,506)(465,507)(466,511)(467,512)(468,513)(469,499)(470,500)(471,501)(472,496)(473,497)(474,498)(475,502)(476,503)(477,504)(478,490)(479,491)(480,492)(481,487)(482,488)(483,489)(484,493)(485,494)(486,495)(541,643)(542,644)(543,645)(544,640)(545,641)(546,642)(547,646)(548,647)(549,648)(550,634)(551,635)(552,636)(553,631)(554,632)(555,633)(556,637)(557,638)(558,639)(559,625)(560,626)(561,627)(562,622)(563,623)(564,624)(565,628)(566,629)(567,630)(568,616)(569,617)(570,618)(571,613)(572,614)(573,615)(574,619)(575,620)(576,621)(577,607)(578,608)(579,609)(580,604)(581,605)(582,606)(583,610)(584,611)(585,612)(586,598)(587,599)(588,600)(589,595)(590,596)(591,597)(592,601)(593,602)(594,603)(649,751)(650,752)(651,753)(652,748)(653,749)(654,750)(655,754)(656,755)(657,756)(658,742)(659,743)(660,744)(661,739)(662,740)(663,741)(664,745)(665,746)(666,747)(667,733)(668,734)(669,735)(670,730)(671,731)(672,732)(673,736)(674,737)(675,738)(676,724)(677,725)(678,726)(679,721)(680,722)(681,723)(682,727)(683,728)(684,729)(685,715)(686,716)(687,717)(688,712)(689,713)(690,714)(691,718)(692,719)(693,720)(694,706)(695,707)(696,708)(697,703)(698,704)(699,705)(700,709)(701,710)(702,711)(757,859)(758,860)(759,861)(760,856)(761,857)(762,858)(763,862)(764,863)(765,864)(766,850)(767,851)(768,852)(769,847)(770,848)(771,849)(772,853)(773,854)(774,855)(775,841)(776,842)(777,843)(778,838)(779,839)(780,840)(781,844)(782,845)(783,846)(784,832)(785,833)(786,834)(787,829)(788,830)(789,831)(790,835)(791,836)(792,837)(793,823)(794,824)(795,825)(796,820)(797,821)(798,822)(799,826)(800,827)(801,828)(802,814)(803,815)(804,816)(805,811)(806,812)(807,813)(808,817)(809,818)(810,819)(865,967)(866,968)(867,969)(868,964)(869,965)(870,966)(871,970)(872,971)(873,972)(874,958)(875,959)(876,960)(877,955)(878,956)(879,957)(880,961)(881,962)(882,963)(883,949)(884,950)(885,951)(886,946)(887,947)(888,948)(889,952)(890,953)(891,954)(892,940)(893,941)(894,942)(895,937)(896,938)(897,939)(898,943)(899,944)(900,945)(901,931)(902,932)(903,933)(904,928)(905,929)(906,930)
(907,934)(908,935)(909,936)(910,922)(911,923)(912,924)(913,919)(914,920)(915,921)(916,925)(917,926)(918,927);;
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*s1*s2*s0*s1*s2*s0*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*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(972)!(  2,  3)(  4, 19)(  5, 21)(  6, 20)(  7, 10)(  8, 12)(  9, 11)( 13, 25)( 14, 27)( 15, 26)( 17, 18)( 23, 24)( 28, 55)( 29, 57)( 30, 56)( 31, 73)( 32, 75)( 33, 74)( 34, 64)
( 35, 66)( 36, 65)( 37, 61)( 38, 63)( 39, 62)( 40, 79)( 41, 81)( 42, 80)( 43, 70)( 44, 72)( 45, 71)( 46, 58)( 47, 60)( 48, 59)( 49, 76)( 50, 78)( 51, 77)( 52, 67)( 53, 69)( 54, 68)( 83, 84)( 85,100)( 86,102)( 87,101)( 88, 91)( 89, 93)( 90, 92)( 94,106)( 95,108)( 96,107)( 98, 99)(104,105)(109,217)(110,219)(111,218)(112,235)(113,237)(114,236)(115,226)(116,228)(117,227)(118,223)(119,225)(120,224)(121,241)(122,243)(123,242)(124,232)(125,234)(126,233)(127,220)(128,222)(129,221)(130,238)(131,240)(132,239)(133,229)(134,231)(135,230)(136,271)(137,273)(138,272)(139,289)(140,291)(141,290)(142,280)(143,282)(144,281)(145,277)(146,279)(147,278)(148,295)(149,297)(150,296)(151,286)(152,288)(153,287)(154,274)(155,276)(156,275)(157,292)(158,294)(159,293)(160,283)(161,285)(162,284)(163,244)(164,246)(165,245)(166,262)(167,264)(168,263)(169,253)(170,255)(171,254)(172,250)(173,252)(174,251)(175,268)(176,270)(177,269)(178,259)(179,261)(180,260)(181,247)(182,249)(183,248)(184,265)(185,267)(186,266)(187,256)(188,258)(189,257)(190,298)(191,300)(192,299)(193,316)(194,318)(195,317)(196,307)(197,309)(198,308)(199,304)(200,306)(201,305)(202,322)(203,324)(204,323)(205,313)(206,315)(207,314)(208,301)(209,303)(210,302)(211,319)(212,321)(213,320)(214,310)(215,312)(216,311)(325,865)(326,867)(327,866)(328,883)(329,885)(330,884)(331,874)(332,876)(333,875)(334,871)(335,873)(336,872)(337,889)(338,891)(339,890)(340,880)(341,882)(342,881)(343,868)(344,870)(345,869)(346,886)(347,888)(348,887)(349,877)(350,879)(351,878)(352,919)(353,921)(354,920)(355,937)(356,939)(357,938)(358,928)(359,930)(360,929)(361,925)(362,927)(363,926)(364,943)(365,945)(366,944)(367,934)(368,936)(369,935)(370,922)(371,924)(372,923)(373,940)(374,942)(375,941)(376,931)(377,933)(378,932)(379,892)(380,894)(381,893)(382,910)(383,912)(384,911)(385,901)(386,903)(387,902)(388,898)(389,900)(390,899)(391,916)(392,918)(393,917)(394,907)(395,909)(396,908)(397,895)(398,897)(399,896)(400,913)(401,915)(402,914)(403,904)(404,906)(405,905)(406,946)(407,948)(408,947)(409,964)(410,966)(411,965)(412,955)(413,957)(414,956)(415,952)(416,954)(417,953)(418,970)(419,972)(420,971)(421,961)(422,963)(423,962)(424,949)(425,951)(426,950)(427,967)(428,969)(429,968)(430,958)(431,960)(432,959)(433,757)(434,759)(435,758)(436,775)(437,777)(438,776)(439,766)(440,768)(441,767)(442,763)(443,765)(444,764)(445,781)(446,783)(447,782)(448,772)(449,774)(450,773)(451,760)(452,762)(453,761)(454,778)(455,780)(456,779)(457,769)(458,771)(459,770)(460,811)(461,813)(462,812)(463,829)(464,831)(465,830)(466,820)(467,822)(468,821)(469,817)(470,819)(471,818)(472,835)(473,837)(474,836)(475,826)(476,828)(477,827)(478,814)(479,816)(480,815)(481,832)(482,834)(483,833)(484,823)(485,825)(486,824)(487,784)(488,786)(489,785)(490,802)(491,804)(492,803)(493,793)(494,795)(495,794)(496,790)(497,792)(498,791)(499,808)(500,810)(501,809)(502,799)(503,801)(504,800)(505,787)(506,789)(507,788)(508,805)(509,807)(510,806)(511,796)(512,798)(513,797)(514,838)(515,840)(516,839)(517,856)(518,858)(519,857)(520,847)(521,849)(522,848)(523,844)(524,846)(525,845)(526,862)(527,864)(528,863)(529,853)(530,855)(531,854)(532,841)(533,843)(534,842)(535,859)(536,861)(537,860)(538,850)(539,852)(540,851)(541,649)(542,651)(543,650)(544,667)(545,669)(546,668)(547,658)(548,660)(549,659)(550,655)(551,657)(552,656)(553,673)(554,675)(555,674)(556,664)(557,666)(558,665)(559,652)(560,654)(561,653)(562,670)(563,672)(564,671)(565,661)(566,663)(567,662)(568,703)(569,705)(570,704)(571,721)(572,723)(573,722)(574,712)(575,714)(576,713)(577,709)(578,711)(579,710)(580,727)(581,729)(582,728)(583,718)(584,720)(585,719)(586,706)(587,708)(588,707)(589,724)(590,726)(591,725)(592,715)(593,717)(594,716)(595,676)(596,678)(597,677)(598,694)(599,696)(600,695)(601,685)(602,687)(603,686)(604,682)(605,684)(606,683)(607,700)(608,702)(609,701)(610,691)(611,693)(612,692)(613,679)(614,681)(615,680)(616,697)(617,699)(618,698)(619,688)(620,690)(621,689)(622,730)(623,732)(624,731)(625,748)(626,750)(627,749)(628,739)(629,741)(630,740)(631,736)(632,738)(633,737)(634,754)(635,756)(636,755)(637,745)(638,747)
(639,746)(640,733)(641,735)(642,734)(643,751)(644,753)(645,752)(646,742)(647,744)(648,743);
s1 := Sym(972)!(  1,334)(  2,340)(  3,337)(  4,336)(  5,342)(  6,339)(  7,335)(  8,341)(  9,338)( 10,325)( 11,331)( 12,328)( 13,327)( 14,333)( 15,330)( 16,326)( 17,332)( 18,329)( 19,343)
( 20,349)( 21,346)( 22,345)( 23,351)( 24,348)( 25,344)( 26,350)( 27,347)( 28,361)( 29,367)( 30,364)( 31,363)( 32,369)( 33,366)( 34,362)( 35,368)( 36,365)( 37,352)( 38,358)( 39,355)( 40,354)( 41,360)( 42,357)( 43,353)( 44,359)( 45,356)( 46,370)( 47,376)( 48,373)( 49,372)( 50,378)( 51,375)( 52,371)( 53,377)( 54,374)( 55,415)( 56,421)( 57,418)( 58,417)( 59,423)( 60,420)( 61,416)( 62,422)( 63,419)( 64,406)( 65,412)( 66,409)( 67,408)( 68,414)( 69,411)( 70,407)( 71,413)( 72,410)( 73,424)( 74,430)( 75,427)( 76,426)( 77,432)( 78,429)( 79,425)( 80,431)( 81,428)( 82,388)( 83,394)( 84,391)( 85,390)( 86,396)( 87,393)( 88,389)( 89,395)( 90,392)( 91,379)( 92,385)( 93,382)( 94,381)( 95,387)( 96,384)( 97,380)( 98,386)( 99,383)(100,397)(101,403)(102,400)(103,399)(104,405)(105,402)(106,398)(107,404)(108,401)(109,550)(110,556)(111,553)(112,552)(113,558)(114,555)(115,551)(116,557)(117,554)(118,541)(119,547)(120,544)(121,543)(122,549)(123,546)(124,542)(125,548)(126,545)(127,559)(128,565)(129,562)(130,561)(131,567)(132,564)(133,560)(134,566)(135,563)(136,577)(137,583)(138,580)(139,579)(140,585)(141,582)(142,578)(143,584)(144,581)(145,568)(146,574)(147,571)(148,570)(149,576)(150,573)(151,569)(152,575)(153,572)(154,586)(155,592)(156,589)(157,588)(158,594)(159,591)(160,587)(161,593)(162,590)(163,631)(164,637)(165,634)(166,633)(167,639)(168,636)(169,632)(170,638)(171,635)(172,622)(173,628)(174,625)(175,624)(176,630)(177,627)(178,623)(179,629)(180,626)(181,640)(182,646)(183,643)(184,642)(185,648)(186,645)(187,641)(188,647)(189,644)(190,604)(191,610)(192,607)(193,606)(194,612)(195,609)(196,605)(197,611)(198,608)(199,595)(200,601)(201,598)(202,597)(203,603)(204,600)(205,596)(206,602)(207,599)(208,613)(209,619)(210,616)(211,615)(212,621)(213,618)(214,614)(215,620)(216,617)(217,442)(218,448)(219,445)(220,444)(221,450)(222,447)(223,443)(224,449)(225,446)(226,433)(227,439)(228,436)(229,435)(230,441)(231,438)(232,434)(233,440)(234,437)(235,451)(236,457)(237,454)(238,453)(239,459)(240,456)(241,452)(242,458)(243,455)(244,469)(245,475)(246,472)(247,471)(248,477)(249,474)(250,470)(251,476)(252,473)(253,460)(254,466)(255,463)(256,462)(257,468)(258,465)(259,461)(260,467)(261,464)(262,478)(263,484)(264,481)(265,480)(266,486)(267,483)(268,479)(269,485)(270,482)(271,523)(272,529)(273,526)(274,525)(275,531)(276,528)(277,524)(278,530)(279,527)(280,514)(281,520)(282,517)(283,516)(284,522)(285,519)(286,515)(287,521)(288,518)(289,532)(290,538)(291,535)(292,534)(293,540)(294,537)(295,533)(296,539)(297,536)(298,496)(299,502)(300,499)(301,498)(302,504)(303,501)(304,497)(305,503)(306,500)(307,487)(308,493)(309,490)(310,489)(311,495)(312,492)(313,488)(314,494)(315,491)(316,505)(317,511)(318,508)(319,507)(320,513)(321,510)(322,506)(323,512)(324,509)(649,874)(650,880)(651,877)(652,876)(653,882)(654,879)(655,875)(656,881)(657,878)(658,865)(659,871)(660,868)(661,867)(662,873)(663,870)(664,866)(665,872)(666,869)(667,883)(668,889)(669,886)(670,885)(671,891)(672,888)(673,884)(674,890)(675,887)(676,901)(677,907)(678,904)(679,903)(680,909)(681,906)(682,902)(683,908)(684,905)(685,892)(686,898)(687,895)(688,894)(689,900)(690,897)(691,893)(692,899)(693,896)(694,910)(695,916)(696,913)(697,912)(698,918)(699,915)(700,911)(701,917)(702,914)(703,955)(704,961)(705,958)(706,957)(707,963)(708,960)(709,956)(710,962)(711,959)(712,946)(713,952)(714,949)(715,948)(716,954)(717,951)(718,947)(719,953)(720,950)(721,964)(722,970)(723,967)(724,966)(725,972)(726,969)(727,965)(728,971)(729,968)(730,928)(731,934)(732,931)(733,930)(734,936)(735,933)(736,929)(737,935)(738,932)(739,919)(740,925)(741,922)(742,921)(743,927)(744,924)(745,920)(746,926)(747,923)(748,937)(749,943)(750,940)(751,939)(752,945)(753,942)(754,938)(755,944)(756,941)(757,766)(758,772)(759,769)(760,768)(761,774)(762,771)(763,767)(764,773)(765,770)(776,781)(777,778)(779,783)(784,793)(785,799)(786,796)(787,795)(788,801)(789,798)(790,794)(791,800)(792,797)(803,808)(804,805)(806,810)(811,847)(812,853)(813,850)(814,849)(815,855)(816,852)(817,848)(818,854)(819,851)(820,838)(821,844)(822,841)(823,840)(824,846)(825,843)(826,839)(827,845)
(828,842)(829,856)(830,862)(831,859)(832,858)(833,864)(834,861)(835,857)(836,863)(837,860);
s2 := Sym(972)!(  1,103)(  2,104)(  3,105)(  4,100)(  5,101)(  6,102)(  7,106)(  8,107)(  9,108)( 10, 94)( 11, 95)( 12, 96)( 13, 91)( 14, 92)( 15, 93)( 16, 97)( 17, 98)( 18, 99)( 19, 85)
( 20, 86)( 21, 87)( 22, 82)( 23, 83)( 24, 84)( 25, 88)( 26, 89)( 27, 90)( 28, 76)( 29, 77)( 30, 78)( 31, 73)( 32, 74)( 33, 75)( 34, 79)( 35, 80)( 36, 81)( 37, 67)( 38, 68)( 39, 69)( 40, 64)( 41, 65)( 42, 66)( 43, 70)( 44, 71)( 45, 72)( 46, 58)( 47, 59)( 48, 60)( 49, 55)( 50, 56)( 51, 57)( 52, 61)( 53, 62)( 54, 63)(109,211)(110,212)(111,213)(112,208)(113,209)(114,210)(115,214)(116,215)(117,216)(118,202)(119,203)(120,204)(121,199)(122,200)(123,201)(124,205)(125,206)(126,207)(127,193)(128,194)(129,195)(130,190)(131,191)(132,192)(133,196)(134,197)(135,198)(136,184)(137,185)(138,186)(139,181)(140,182)(141,183)(142,187)(143,188)(144,189)(145,175)(146,176)(147,177)(148,172)(149,173)(150,174)(151,178)(152,179)(153,180)(154,166)(155,167)(156,168)(157,163)(158,164)(159,165)(160,169)(161,170)(162,171)(217,319)(218,320)(219,321)(220,316)(221,317)(222,318)(223,322)(224,323)(225,324)(226,310)(227,311)(228,312)(229,307)(230,308)(231,309)(232,313)(233,314)(234,315)(235,301)(236,302)(237,303)(238,298)(239,299)(240,300)(241,304)(242,305)(243,306)(244,292)(245,293)(246,294)(247,289)(248,290)(249,291)(250,295)(251,296)(252,297)(253,283)(254,284)(255,285)(256,280)(257,281)(258,282)(259,286)(260,287)(261,288)(262,274)(263,275)(264,276)(265,271)(266,272)(267,273)(268,277)(269,278)(270,279)(325,427)(326,428)(327,429)(328,424)(329,425)(330,426)(331,430)(332,431)(333,432)(334,418)(335,419)(336,420)(337,415)(338,416)(339,417)(340,421)(341,422)(342,423)(343,409)(344,410)(345,411)(346,406)(347,407)(348,408)(349,412)(350,413)(351,414)(352,400)(353,401)(354,402)(355,397)(356,398)(357,399)(358,403)(359,404)(360,405)(361,391)(362,392)(363,393)(364,388)(365,389)(366,390)(367,394)(368,395)(369,396)(370,382)(371,383)(372,384)(373,379)(374,380)(375,381)(376,385)(377,386)(378,387)(433,535)(434,536)(435,537)(436,532)(437,533)(438,534)(439,538)(440,539)(441,540)(442,526)(443,527)(444,528)(445,523)(446,524)(447,525)(448,529)(449,530)(450,531)(451,517)(452,518)(453,519)(454,514)(455,515)(456,516)(457,520)(458,521)(459,522)(460,508)(461,509)(462,510)(463,505)(464,506)(465,507)(466,511)(467,512)(468,513)(469,499)(470,500)(471,501)(472,496)(473,497)(474,498)(475,502)(476,503)(477,504)(478,490)(479,491)(480,492)(481,487)(482,488)(483,489)(484,493)(485,494)(486,495)(541,643)(542,644)(543,645)(544,640)(545,641)(546,642)(547,646)(548,647)(549,648)(550,634)(551,635)(552,636)(553,631)(554,632)(555,633)(556,637)(557,638)(558,639)(559,625)(560,626)(561,627)(562,622)(563,623)(564,624)(565,628)(566,629)(567,630)(568,616)(569,617)(570,618)(571,613)(572,614)(573,615)(574,619)(575,620)(576,621)(577,607)(578,608)(579,609)(580,604)(581,605)(582,606)(583,610)(584,611)(585,612)(586,598)(587,599)(588,600)(589,595)(590,596)(591,597)(592,601)(593,602)(594,603)(649,751)(650,752)(651,753)(652,748)(653,749)(654,750)(655,754)(656,755)(657,756)(658,742)(659,743)(660,744)(661,739)(662,740)(663,741)(664,745)(665,746)(666,747)(667,733)(668,734)(669,735)(670,730)(671,731)(672,732)(673,736)(674,737)(675,738)(676,724)(677,725)(678,726)(679,721)(680,722)(681,723)(682,727)(683,728)(684,729)(685,715)(686,716)(687,717)(688,712)(689,713)(690,714)(691,718)(692,719)(693,720)(694,706)(695,707)(696,708)(697,703)(698,704)(699,705)(700,709)(701,710)(702,711)(757,859)(758,860)(759,861)(760,856)(761,857)(762,858)(763,862)(764,863)(765,864)(766,850)(767,851)(768,852)(769,847)(770,848)(771,849)(772,853)(773,854)(774,855)(775,841)(776,842)(777,843)(778,838)(779,839)(780,840)(781,844)(782,845)(783,846)(784,832)(785,833)(786,834)(787,829)(788,830)(789,831)(790,835)(791,836)(792,837)(793,823)(794,824)(795,825)(796,820)(797,821)(798,822)(799,826)(800,827)(801,828)(802,814)(803,815)(804,816)(805,811)(806,812)(807,813)(808,817)(809,818)(810,819)(865,967)(866,968)(867,969)(868,964)(869,965)(870,966)(871,970)(872,971)(873,972)(874,958)(875,959)(876,960)(877,955)(878,956)(879,957)(880,961)(881,962)(882,963)(883,949)(884,950)(885,951)(886,946)(887,947)(888,948)(889,952)(890,953)(891,954)(892,940)(893,941)(894,942)(895,937)(896,938)(897,939)(898,943)(899,944)(900,945)(901,931)(902,932)(903,933)(904,928)(905,929)
(906,930)(907,934)(908,935)(909,936)(910,922)(911,923)(912,924)(913,919)(914,920)(915,921)(916,925)(917,926)(918,927);
poly := sub<Sym(972)|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*s1*s2*s0*s1*s2*s0*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*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s2 >;

References : None.
to this polytope

Polytope of Type {9,12}

Twisty Puzzle