Polytope of Type {12,9}

Play with this polytope as a twisty puzzle

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

Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope

Polytope of Type {12,9}

Twisty Puzzle