Polytope of Type {9,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {9,12}*864
if this polytope has a name.
Group : SmallGroup(864,2202)
Rank : 3
Schlafli Type : {9,12}
Number of vertices, edges, etc : 36, 216, 48
Order of s0s1s2 : 72
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {9,12,2} of size 1728
Vertex Figure Of :
   {2,9,12} of size 1728
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {9,6}*432
   3-fold quotients : {3,12}*288
   6-fold quotients : {3,6}*144
   8-fold quotients : {9,6}*108
   9-fold quotients : {3,12}*96
   18-fold quotients : {3,6}*48
   24-fold quotients : {9,2}*36, {3,6}*36
   36-fold quotients : {3,3}*24
   72-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   2-fold covers : {18,12}*1728a
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 3.
      16 facets:
         16 of {9}*18
      18 vertex figures:
         9 of {12}*24
         9 of {4}*8

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

Twisty Puzzle