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}*1944b
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 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Self-Petrie
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}*648a
   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*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 3.
      36 facets:
         36 of {9}*18
      27 vertex figures:
         27 of {12}*24
   P/N, where N=<s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s1*s2*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> 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, s0*s2*s1*s0*s2*s1*s0*s2*s1> 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*s0*s1*s2*s1*s0*s2*s1*s0*s2> of order 9.
      12 facets:
         12 of {9}*18
      21 vertex figures:
         3 of {12}*24
         18 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s1*s2*s1*s0*s2*s1*s2> 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*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> 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, 82)(  2, 83)(  3, 84)(  4, 88)(  5, 89)(  6, 90)(  7, 85)(  8, 86)(  9, 87)( 10,100)( 11,101)( 12,102)( 13,106)( 14,107)( 15,108)( 16,103)( 17,104)( 18,105)( 19, 91)( 20, 92)
( 21, 93)( 22, 97)( 23, 98)( 24, 99)( 25, 94)( 26, 95)( 27, 96)( 28, 55)( 29, 56)( 30, 57)( 31, 61)( 32, 62)( 33, 63)( 34, 58)( 35, 59)( 36, 60)( 37, 73)( 38, 74)( 39, 75)( 40, 79)( 41, 80)( 42, 81)( 43, 76)( 44, 77)( 45, 78)( 46, 64)( 47, 65)( 48, 66)( 49, 70)( 50, 71)( 51, 72)( 52, 67)( 53, 68)( 54, 69)(109,190)(110,191)(111,192)(112,196)(113,197)(114,198)(115,193)(116,194)(117,195)(118,208)(119,209)(120,210)(121,214)(122,215)(123,216)(124,211)(125,212)(126,213)(127,199)(128,200)(129,201)(130,205)(131,206)(132,207)(133,202)(134,203)(135,204)(136,163)(137,164)(138,165)(139,169)(140,170)(141,171)(142,166)(143,167)(144,168)(145,181)(146,182)(147,183)(148,187)(149,188)(150,189)(151,184)(152,185)(153,186)(154,172)(155,173)(156,174)(157,178)(158,179)(159,180)(160,175)(161,176)(162,177)(217,298)(218,299)(219,300)(220,304)(221,305)(222,306)(223,301)(224,302)(225,303)(226,316)(227,317)(228,318)(229,322)(230,323)(231,324)(232,319)(233,320)(234,321)(235,307)(236,308)(237,309)(238,313)(239,314)(240,315)(241,310)(242,311)(243,312)(244,271)(245,272)(246,273)(247,277)(248,278)(249,279)(250,274)(251,275)(252,276)(253,289)(254,290)(255,291)(256,295)(257,296)(258,297)(259,292)(260,293)(261,294)(262,280)(263,281)(264,282)(265,286)(266,287)(267,288)(268,283)(269,284)(270,285)(325,406)(326,407)(327,408)(328,412)(329,413)(330,414)(331,409)(332,410)(333,411)(334,424)(335,425)(336,426)(337,430)(338,431)(339,432)(340,427)(341,428)(342,429)(343,415)(344,416)(345,417)(346,421)(347,422)(348,423)(349,418)(350,419)(351,420)(352,379)(353,380)(354,381)(355,385)(356,386)(357,387)(358,382)(359,383)(360,384)(361,397)(362,398)(363,399)(364,403)(365,404)(366,405)(367,400)(368,401)(369,402)(370,388)(371,389)(372,390)(373,394)(374,395)(375,396)(376,391)(377,392)(378,393)(433,514)(434,515)(435,516)(436,520)(437,521)(438,522)(439,517)(440,518)(441,519)(442,532)(443,533)(444,534)(445,538)(446,539)(447,540)(448,535)(449,536)(450,537)(451,523)(452,524)(453,525)(454,529)(455,530)(456,531)(457,526)(458,527)(459,528)(460,487)(461,488)(462,489)(463,493)(464,494)(465,495)(466,490)(467,491)(468,492)(469,505)(470,506)(471,507)(472,511)(473,512)(474,513)(475,508)(476,509)(477,510)(478,496)(479,497)(480,498)(481,502)(482,503)(483,504)(484,499)(485,500)(486,501)(541,622)(542,623)(543,624)(544,628)(545,629)(546,630)(547,625)(548,626)(549,627)(550,640)(551,641)(552,642)(553,646)(554,647)(555,648)(556,643)(557,644)(558,645)(559,631)(560,632)(561,633)(562,637)(563,638)(564,639)(565,634)(566,635)(567,636)(568,595)(569,596)(570,597)(571,601)(572,602)(573,603)(574,598)(575,599)(576,600)(577,613)(578,614)(579,615)(580,619)(581,620)(582,621)(583,616)(584,617)(585,618)(586,604)(587,605)(588,606)(589,610)(590,611)(591,612)(592,607)(593,608)(594,609)(649,730)(650,731)(651,732)(652,736)(653,737)(654,738)(655,733)(656,734)(657,735)(658,748)(659,749)(660,750)(661,754)(662,755)(663,756)(664,751)(665,752)(666,753)(667,739)(668,740)(669,741)(670,745)(671,746)(672,747)(673,742)(674,743)(675,744)(676,703)(677,704)(678,705)(679,709)(680,710)(681,711)(682,706)(683,707)(684,708)(685,721)(686,722)(687,723)(688,727)(689,728)(690,729)(691,724)(692,725)(693,726)(694,712)(695,713)(696,714)(697,718)(698,719)(699,720)(700,715)(701,716)(702,717)(757,838)(758,839)(759,840)(760,844)(761,845)(762,846)(763,841)(764,842)(765,843)(766,856)(767,857)(768,858)(769,862)(770,863)(771,864)(772,859)(773,860)(774,861)(775,847)(776,848)(777,849)(778,853)(779,854)(780,855)(781,850)(782,851)(783,852)(784,811)(785,812)(786,813)(787,817)(788,818)(789,819)(790,814)(791,815)(792,816)(793,829)(794,830)(795,831)(796,835)(797,836)(798,837)(799,832)(800,833)(801,834)(802,820)(803,821)(804,822)(805,826)(806,827)(807,828)(808,823)(809,824)(810,825)(865,946)(866,947)(867,948)(868,952)(869,953)(870,954)(871,949)(872,950)(873,951)(874,964)(875,965)(876,966)(877,970)(878,971)(879,972)(880,967)(881,968)(882,969)(883,955)(884,956)(885,957)(886,961)(887,962)(888,963)(889,958)(890,959)(891,960)(892,919)(893,920)(894,921)(895,925)(896,926)(897,927)(898,922)(899,923)(900,924)(901,937)(902,938)(903,939)(904,943)(905,944)(906,945)
(907,940)(908,941)(909,942)(910,928)(911,929)(912,930)(913,934)(914,935)(915,936)(916,931)(917,932)(918,933);;
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*s0*s1*s2*s1*s0*s1*s2*s1*s0*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*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*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, 82)(  2, 83)(  3, 84)(  4, 88)(  5, 89)(  6, 90)(  7, 85)(  8, 86)(  9, 87)( 10,100)( 11,101)( 12,102)( 13,106)( 14,107)( 15,108)( 16,103)( 17,104)( 18,105)( 19, 91)
( 20, 92)( 21, 93)( 22, 97)( 23, 98)( 24, 99)( 25, 94)( 26, 95)( 27, 96)( 28, 55)( 29, 56)( 30, 57)( 31, 61)( 32, 62)( 33, 63)( 34, 58)( 35, 59)( 36, 60)( 37, 73)( 38, 74)( 39, 75)( 40, 79)( 41, 80)( 42, 81)( 43, 76)( 44, 77)( 45, 78)( 46, 64)( 47, 65)( 48, 66)( 49, 70)( 50, 71)( 51, 72)( 52, 67)( 53, 68)( 54, 69)(109,190)(110,191)(111,192)(112,196)(113,197)(114,198)(115,193)(116,194)(117,195)(118,208)(119,209)(120,210)(121,214)(122,215)(123,216)(124,211)(125,212)(126,213)(127,199)(128,200)(129,201)(130,205)(131,206)(132,207)(133,202)(134,203)(135,204)(136,163)(137,164)(138,165)(139,169)(140,170)(141,171)(142,166)(143,167)(144,168)(145,181)(146,182)(147,183)(148,187)(149,188)(150,189)(151,184)(152,185)(153,186)(154,172)(155,173)(156,174)(157,178)(158,179)(159,180)(160,175)(161,176)(162,177)(217,298)(218,299)(219,300)(220,304)(221,305)(222,306)(223,301)(224,302)(225,303)(226,316)(227,317)(228,318)(229,322)(230,323)(231,324)(232,319)(233,320)(234,321)(235,307)(236,308)(237,309)(238,313)(239,314)(240,315)(241,310)(242,311)(243,312)(244,271)(245,272)(246,273)(247,277)(248,278)(249,279)(250,274)(251,275)(252,276)(253,289)(254,290)(255,291)(256,295)(257,296)(258,297)(259,292)(260,293)(261,294)(262,280)(263,281)(264,282)(265,286)(266,287)(267,288)(268,283)(269,284)(270,285)(325,406)(326,407)(327,408)(328,412)(329,413)(330,414)(331,409)(332,410)(333,411)(334,424)(335,425)(336,426)(337,430)(338,431)(339,432)(340,427)(341,428)(342,429)(343,415)(344,416)(345,417)(346,421)(347,422)(348,423)(349,418)(350,419)(351,420)(352,379)(353,380)(354,381)(355,385)(356,386)(357,387)(358,382)(359,383)(360,384)(361,397)(362,398)(363,399)(364,403)(365,404)(366,405)(367,400)(368,401)(369,402)(370,388)(371,389)(372,390)(373,394)(374,395)(375,396)(376,391)(377,392)(378,393)(433,514)(434,515)(435,516)(436,520)(437,521)(438,522)(439,517)(440,518)(441,519)(442,532)(443,533)(444,534)(445,538)(446,539)(447,540)(448,535)(449,536)(450,537)(451,523)(452,524)(453,525)(454,529)(455,530)(456,531)(457,526)(458,527)(459,528)(460,487)(461,488)(462,489)(463,493)(464,494)(465,495)(466,490)(467,491)(468,492)(469,505)(470,506)(471,507)(472,511)(473,512)(474,513)(475,508)(476,509)(477,510)(478,496)(479,497)(480,498)(481,502)(482,503)(483,504)(484,499)(485,500)(486,501)(541,622)(542,623)(543,624)(544,628)(545,629)(546,630)(547,625)(548,626)(549,627)(550,640)(551,641)(552,642)(553,646)(554,647)(555,648)(556,643)(557,644)(558,645)(559,631)(560,632)(561,633)(562,637)(563,638)(564,639)(565,634)(566,635)(567,636)(568,595)(569,596)(570,597)(571,601)(572,602)(573,603)(574,598)(575,599)(576,600)(577,613)(578,614)(579,615)(580,619)(581,620)(582,621)(583,616)(584,617)(585,618)(586,604)(587,605)(588,606)(589,610)(590,611)(591,612)(592,607)(593,608)(594,609)(649,730)(650,731)(651,732)(652,736)(653,737)(654,738)(655,733)(656,734)(657,735)(658,748)(659,749)(660,750)(661,754)(662,755)(663,756)(664,751)(665,752)(666,753)(667,739)(668,740)(669,741)(670,745)(671,746)(672,747)(673,742)(674,743)(675,744)(676,703)(677,704)(678,705)(679,709)(680,710)(681,711)(682,706)(683,707)(684,708)(685,721)(686,722)(687,723)(688,727)(689,728)(690,729)(691,724)(692,725)(693,726)(694,712)(695,713)(696,714)(697,718)(698,719)(699,720)(700,715)(701,716)(702,717)(757,838)(758,839)(759,840)(760,844)(761,845)(762,846)(763,841)(764,842)(765,843)(766,856)(767,857)(768,858)(769,862)(770,863)(771,864)(772,859)(773,860)(774,861)(775,847)(776,848)(777,849)(778,853)(779,854)(780,855)(781,850)(782,851)(783,852)(784,811)(785,812)(786,813)(787,817)(788,818)(789,819)(790,814)(791,815)(792,816)(793,829)(794,830)(795,831)(796,835)(797,836)(798,837)(799,832)(800,833)(801,834)(802,820)(803,821)(804,822)(805,826)(806,827)(807,828)(808,823)(809,824)(810,825)(865,946)(866,947)(867,948)(868,952)(869,953)(870,954)(871,949)(872,950)(873,951)(874,964)(875,965)(876,966)(877,970)(878,971)(879,972)(880,967)(881,968)(882,969)(883,955)(884,956)(885,957)(886,961)(887,962)(888,963)(889,958)(890,959)(891,960)(892,919)(893,920)(894,921)(895,925)(896,926)(897,927)(898,922)(899,923)(900,924)(901,937)(902,938)(903,939)(904,943)(905,944)
(906,945)(907,940)(908,941)(909,942)(910,928)(911,929)(912,930)(913,934)(914,935)(915,936)(916,931)(917,932)(918,933);
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, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*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*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle