Polytope of Type {9,9}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,9}*1944b
if this polytope has a name.
Group : SmallGroup(1944,3453)
Rank : 3
Schlafli Type : {9,9}
Number of vertices, edges, etc : 108, 486, 108
Order of s0s1s2 : 12
Order of s0s1s2s1 : 9
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Dual
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 : {9,9}*648a
   81-fold quotients : {3,3}*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*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s1> of order 3.
      36 facets:
         36 of {9}*18
      36 vertex figures:
         36 of {9}*18
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 3.
      36 facets:
         36 of {9}*18
      36 vertex figures:
         36 of {9}*18
   P/N, where N=<s0*s2*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1> of order 3.
      36 facets:
         36 of {9}*18
      36 vertex figures:
         36 of {9}*18
   P/N, where N=<s0*s1*s0*s1*s0*s1> of order 3.
      54 facets:
         27 of {3}*6
         27 of {9}*18
      54 vertex figures:
         27 of {9}*18
         27 of {3}*6
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      36 facets:
         36 of {9}*18
      36 vertex figures:
         36 of {9}*18
   P/N, where N=<s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2> of order 9.
      24 facets:
         18 of {3}*6
         6 of {9}*18
      24 vertex figures:
         18 of {3}*6
         6 of {9}*18
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1> of order 9.
      12 facets:
         12 of {9}*18
      12 vertex figures:
         12 of {9}*18
   P/N, where N=<s0*s1*s0*s1*s0*s1, s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 9.
      18 facets:
         9 of {3}*6
         9 of {9}*18
      18 vertex figures:
         9 of {9}*18
         9 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1, s1*s2*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s0*s2> of order 27.
      10 facets:
         9 of {3}*6
         1 of {9}*18
      10 vertex figures:
         9 of {3}*6
         1 of {9}*18

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

Twisty Puzzle