Polytope of Type {6,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,24}*1728g
if this polytope has a name.
Group : SmallGroup(1728,46313)
Rank : 3
Schlafli Type : {6,24}
Number of vertices, edges, etc : 36, 432, 144
Order of s0s1s2 : 6
Order of s0s1s2s1 : 24
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 : {6,12}*864c
   3-fold quotients : {6,24}*576c, {6,24}*576d
   6-fold quotients : {6,12}*288a, {6,12}*288b
   8-fold quotients : {6,6}*216d
   9-fold quotients : {6,8}*192c
   12-fold quotients : {3,12}*144, {6,12}*144d
   18-fold quotients : {6,4}*96
   24-fold quotients : {6,6}*72a, {6,6}*72b, {6,6}*72c
   36-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   48-fold quotients : {3,6}*36, {6,3}*36
   72-fold quotients : {3,4}*24, {2,6}*24, {6,2}*24
   144-fold quotients : {2,3}*12, {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*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0> of order 2.
      72 facets:
         72 of {6}*12
      18 vertex figures:
         18 of {24}*48
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s2> of order 3.
      48 facets:
         48 of {6}*12
      24 vertex figures:
         6 of {24}*48
         18 of {8}*16
   P/N, where N=<s0*s2*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2> of order 3.
      48 facets:
         48 of {6}*12
      12 vertex figures:
         12 of {24}*48

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

Twisty Puzzle