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}*1944a
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 : 4
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}*648a
   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*s2*s1*s0*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*s0*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1> 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=<s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s0*s2*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, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 9.
      9 facets:
         9 of {12}*24
      24 vertex figures:
         18 of {3}*6
         6 of {9}*18
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1, s0*s1*s0*s2*s1*s0*s1*s2*s1> 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, s1*s0*s1*s0*s2*s1*s0*s1*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*s2*s1*s0*s2*s1*s0*s1*s2*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 := (  1,649)(  2,667)(  3,658)(  4,655)(  5,673)(  6,664)(  7,652)(  8,670)(  9,661)( 10,651)( 11,669)( 12,660)( 13,657)( 14,675)( 15,666)( 16,654)( 17,672)( 18,663)( 19,650)( 20,668)
( 21,659)( 22,656)( 23,674)( 24,665)( 25,653)( 26,671)( 27,662)( 28,730)( 29,748)( 30,739)( 31,736)( 32,754)( 33,745)( 34,733)( 35,751)( 36,742)( 37,732)( 38,750)( 39,741)( 40,738)( 41,756)( 42,747)( 43,735)( 44,753)( 45,744)( 46,731)( 47,749)( 48,740)( 49,737)( 50,755)( 51,746)( 52,734)( 53,752)( 54,743)( 55,703)( 56,721)( 57,712)( 58,709)( 59,727)( 60,718)( 61,706)( 62,724)( 63,715)( 64,705)( 65,723)( 66,714)( 67,711)( 68,729)( 69,720)( 70,708)( 71,726)( 72,717)( 73,704)( 74,722)( 75,713)( 76,710)( 77,728)( 78,719)( 79,707)( 80,725)( 81,716)( 82,676)( 83,694)( 84,685)( 85,682)( 86,700)( 87,691)( 88,679)( 89,697)( 90,688)( 91,678)( 92,696)( 93,687)( 94,684)( 95,702)( 96,693)( 97,681)( 98,699)( 99,690)(100,677)(101,695)(102,686)(103,683)(104,701)(105,692)(106,680)(107,698)(108,689)(109,865)(110,883)(111,874)(112,871)(113,889)(114,880)(115,868)(116,886)(117,877)(118,867)(119,885)(120,876)(121,873)(122,891)(123,882)(124,870)(125,888)(126,879)(127,866)(128,884)(129,875)(130,872)(131,890)(132,881)(133,869)(134,887)(135,878)(136,946)(137,964)(138,955)(139,952)(140,970)(141,961)(142,949)(143,967)(144,958)(145,948)(146,966)(147,957)(148,954)(149,972)(150,963)(151,951)(152,969)(153,960)(154,947)(155,965)(156,956)(157,953)(158,971)(159,962)(160,950)(161,968)(162,959)(163,919)(164,937)(165,928)(166,925)(167,943)(168,934)(169,922)(170,940)(171,931)(172,921)(173,939)(174,930)(175,927)(176,945)(177,936)(178,924)(179,942)(180,933)(181,920)(182,938)(183,929)(184,926)(185,944)(186,935)(187,923)(188,941)(189,932)(190,892)(191,910)(192,901)(193,898)(194,916)(195,907)(196,895)(197,913)(198,904)(199,894)(200,912)(201,903)(202,900)(203,918)(204,909)(205,897)(206,915)(207,906)(208,893)(209,911)(210,902)(211,899)(212,917)(213,908)(214,896)(215,914)(216,905)(217,757)(218,775)(219,766)(220,763)(221,781)(222,772)(223,760)(224,778)(225,769)(226,759)(227,777)(228,768)(229,765)(230,783)(231,774)(232,762)(233,780)(234,771)(235,758)(236,776)(237,767)(238,764)(239,782)(240,773)(241,761)(242,779)(243,770)(244,838)(245,856)(246,847)(247,844)(248,862)(249,853)(250,841)(251,859)(252,850)(253,840)(254,858)(255,849)(256,846)(257,864)(258,855)(259,843)(260,861)(261,852)(262,839)(263,857)(264,848)(265,845)(266,863)(267,854)(268,842)(269,860)(270,851)(271,811)(272,829)(273,820)(274,817)(275,835)(276,826)(277,814)(278,832)(279,823)(280,813)(281,831)(282,822)(283,819)(284,837)(285,828)(286,816)(287,834)(288,825)(289,812)(290,830)(291,821)(292,818)(293,836)(294,827)(295,815)(296,833)(297,824)(298,784)(299,802)(300,793)(301,790)(302,808)(303,799)(304,787)(305,805)(306,796)(307,786)(308,804)(309,795)(310,792)(311,810)(312,801)(313,789)(314,807)(315,798)(316,785)(317,803)(318,794)(319,791)(320,809)(321,800)(322,788)(323,806)(324,797)(326,343)(327,334)(328,331)(329,349)(330,340)(332,346)(333,337)(335,345)(338,351)(339,342)(341,348)(347,350)(352,406)(353,424)(354,415)(355,412)(356,430)(357,421)(358,409)(359,427)(360,418)(361,408)(362,426)(363,417)(364,414)(365,432)(366,423)(367,411)(368,429)(369,420)(370,407)(371,425)(372,416)(373,413)(374,431)(375,422)(376,410)(377,428)(378,419)(380,397)(381,388)(382,385)(383,403)(384,394)(386,400)(387,391)(389,399)(392,405)(393,396)(395,402)(401,404)(433,541)(434,559)(435,550)(436,547)(437,565)(438,556)(439,544)(440,562)(441,553)(442,543)(443,561)(444,552)(445,549)(446,567)(447,558)(448,546)(449,564)(450,555)(451,542)(452,560)(453,551)(454,548)(455,566)(456,557)(457,545)(458,563)(459,554)(460,622)(461,640)(462,631)(463,628)(464,646)(465,637)(466,625)(467,643)(468,634)(469,624)(470,642)(471,633)(472,630)(473,648)(474,639)(475,627)(476,645)(477,636)(478,623)(479,641)(480,632)(481,629)(482,647)(483,638)(484,626)(485,644)(486,635)(487,595)(488,613)(489,604)(490,601)(491,619)(492,610)(493,598)(494,616)(495,607)(496,597)(497,615)(498,606)(499,603)(500,621)(501,612)(502,600)(503,618)(504,609)(505,596)(506,614)(507,605)(508,602)(509,620)(510,611)(511,599)(512,617)(513,608)(514,568)(515,586)(516,577)(517,574)(518,592)(519,583)(520,571)(521,589)(522,580)(523,570)(524,588)(525,579)(526,576)(527,594)(528,585)(529,573)(530,591)(531,582)
(532,569)(533,587)(534,578)(535,575)(536,593)(537,584)(538,572)(539,590)(540,581);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*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)!(  1,649)(  2,667)(  3,658)(  4,655)(  5,673)(  6,664)(  7,652)(  8,670)(  9,661)( 10,651)( 11,669)( 12,660)( 13,657)( 14,675)( 15,666)( 16,654)( 17,672)( 18,663)( 19,650)
( 20,668)( 21,659)( 22,656)( 23,674)( 24,665)( 25,653)( 26,671)( 27,662)( 28,730)( 29,748)( 30,739)( 31,736)( 32,754)( 33,745)( 34,733)( 35,751)( 36,742)( 37,732)( 38,750)( 39,741)( 40,738)( 41,756)( 42,747)( 43,735)( 44,753)( 45,744)( 46,731)( 47,749)( 48,740)( 49,737)( 50,755)( 51,746)( 52,734)( 53,752)( 54,743)( 55,703)( 56,721)( 57,712)( 58,709)( 59,727)( 60,718)( 61,706)( 62,724)( 63,715)( 64,705)( 65,723)( 66,714)( 67,711)( 68,729)( 69,720)( 70,708)( 71,726)( 72,717)( 73,704)( 74,722)( 75,713)( 76,710)( 77,728)( 78,719)( 79,707)( 80,725)( 81,716)( 82,676)( 83,694)( 84,685)( 85,682)( 86,700)( 87,691)( 88,679)( 89,697)( 90,688)( 91,678)( 92,696)( 93,687)( 94,684)( 95,702)( 96,693)( 97,681)( 98,699)( 99,690)(100,677)(101,695)(102,686)(103,683)(104,701)(105,692)(106,680)(107,698)(108,689)(109,865)(110,883)(111,874)(112,871)(113,889)(114,880)(115,868)(116,886)(117,877)(118,867)(119,885)(120,876)(121,873)(122,891)(123,882)(124,870)(125,888)(126,879)(127,866)(128,884)(129,875)(130,872)(131,890)(132,881)(133,869)(134,887)(135,878)(136,946)(137,964)(138,955)(139,952)(140,970)(141,961)(142,949)(143,967)(144,958)(145,948)(146,966)(147,957)(148,954)(149,972)(150,963)(151,951)(152,969)(153,960)(154,947)(155,965)(156,956)(157,953)(158,971)(159,962)(160,950)(161,968)(162,959)(163,919)(164,937)(165,928)(166,925)(167,943)(168,934)(169,922)(170,940)(171,931)(172,921)(173,939)(174,930)(175,927)(176,945)(177,936)(178,924)(179,942)(180,933)(181,920)(182,938)(183,929)(184,926)(185,944)(186,935)(187,923)(188,941)(189,932)(190,892)(191,910)(192,901)(193,898)(194,916)(195,907)(196,895)(197,913)(198,904)(199,894)(200,912)(201,903)(202,900)(203,918)(204,909)(205,897)(206,915)(207,906)(208,893)(209,911)(210,902)(211,899)(212,917)(213,908)(214,896)(215,914)(216,905)(217,757)(218,775)(219,766)(220,763)(221,781)(222,772)(223,760)(224,778)(225,769)(226,759)(227,777)(228,768)(229,765)(230,783)(231,774)(232,762)(233,780)(234,771)(235,758)(236,776)(237,767)(238,764)(239,782)(240,773)(241,761)(242,779)(243,770)(244,838)(245,856)(246,847)(247,844)(248,862)(249,853)(250,841)(251,859)(252,850)(253,840)(254,858)(255,849)(256,846)(257,864)(258,855)(259,843)(260,861)(261,852)(262,839)(263,857)(264,848)(265,845)(266,863)(267,854)(268,842)(269,860)(270,851)(271,811)(272,829)(273,820)(274,817)(275,835)(276,826)(277,814)(278,832)(279,823)(280,813)(281,831)(282,822)(283,819)(284,837)(285,828)(286,816)(287,834)(288,825)(289,812)(290,830)(291,821)(292,818)(293,836)(294,827)(295,815)(296,833)(297,824)(298,784)(299,802)(300,793)(301,790)(302,808)(303,799)(304,787)(305,805)(306,796)(307,786)(308,804)(309,795)(310,792)(311,810)(312,801)(313,789)(314,807)(315,798)(316,785)(317,803)(318,794)(319,791)(320,809)(321,800)(322,788)(323,806)(324,797)(326,343)(327,334)(328,331)(329,349)(330,340)(332,346)(333,337)(335,345)(338,351)(339,342)(341,348)(347,350)(352,406)(353,424)(354,415)(355,412)(356,430)(357,421)(358,409)(359,427)(360,418)(361,408)(362,426)(363,417)(364,414)(365,432)(366,423)(367,411)(368,429)(369,420)(370,407)(371,425)(372,416)(373,413)(374,431)(375,422)(376,410)(377,428)(378,419)(380,397)(381,388)(382,385)(383,403)(384,394)(386,400)(387,391)(389,399)(392,405)(393,396)(395,402)(401,404)(433,541)(434,559)(435,550)(436,547)(437,565)(438,556)(439,544)(440,562)(441,553)(442,543)(443,561)(444,552)(445,549)(446,567)(447,558)(448,546)(449,564)(450,555)(451,542)(452,560)(453,551)(454,548)(455,566)(456,557)(457,545)(458,563)(459,554)(460,622)(461,640)(462,631)(463,628)(464,646)(465,637)(466,625)(467,643)(468,634)(469,624)(470,642)(471,633)(472,630)(473,648)(474,639)(475,627)(476,645)(477,636)(478,623)(479,641)(480,632)(481,629)(482,647)(483,638)(484,626)(485,644)(486,635)(487,595)(488,613)(489,604)(490,601)(491,619)(492,610)(493,598)(494,616)(495,607)(496,597)(497,615)(498,606)(499,603)(500,621)(501,612)(502,600)(503,618)(504,609)(505,596)(506,614)(507,605)(508,602)(509,620)(510,611)(511,599)(512,617)(513,608)(514,568)(515,586)(516,577)(517,574)(518,592)(519,583)(520,571)(521,589)(522,580)(523,570)(524,588)(525,579)(526,576)(527,594)(528,585)(529,573)(530,591)
(531,582)(532,569)(533,587)(534,578)(535,575)(536,593)(537,584)(538,572)(539,590)(540,581);
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s1*s0*s1*s2*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle