Polytope of Type {24,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1728x
if this polytope has a name.
Group : SmallGroup(1728,33667)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 72, 432, 36
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   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) :
   2-fold quotients : {12,12}*864k
   3-fold quotients : {8,12}*576b
   4-fold quotients : {12,6}*432i
   6-fold quotients : {4,12}*288
   8-fold quotients : {12,6}*216c
   9-fold quotients : {24,4}*192b
   12-fold quotients : {4,6}*144
   18-fold quotients : {12,4}*96a
   24-fold quotients : {4,6}*72
   27-fold quotients : {8,4}*64b
   36-fold quotients : {12,2}*48, {6,4}*48a
   54-fold quotients : {4,4}*32
   72-fold quotients : {6,2}*24
   108-fold quotients : {2,4}*16, {4,2}*16
   144-fold quotients : {3,2}*12
   216-fold quotients : {2,2}*8
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*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 2.
      18 facets:
         18 of {24}*48
      36 vertex figures:
         36 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2> of order 3.
      12 facets:
         12 of {24}*48
      48 vertex figures:
         12 of {12}*24
         36 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      12 facets:
         12 of {24}*48
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s0*s2*s1> of order 3.
      12 facets:
         12 of {24}*48
      24 vertex figures:
         24 of {12}*24

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

Twisty Puzzle