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}*864
if this polytope has a name.
Group : SmallGroup(864,2202)
Rank : 3
Schlafli Type : {12,9}
Number of vertices, edges, etc : 48, 216, 36
Order of s0s1s2 : 72
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {12,9,2} of size 1728
Vertex Figure Of :
   {2,12,9} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,9}*432
   3-fold quotients : {12,3}*288
   6-fold quotients : {6,3}*144
   8-fold quotients : {6,9}*108
   9-fold quotients : {12,3}*96
   18-fold quotients : {6,3}*48
   24-fold quotients : {2,9}*36, {6,3}*36
   36-fold quotients : {3,3}*24
   72-fold quotients : {2,3}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {12,18}*1728a
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      18 facets:
         9 of {4}*8
         9 of {12}*24
      16 vertex figures:
         16 of {9}*18

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

Twisty Puzzle