Polytope of Type {6,48}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,48}*1728f
if this polytope has a name.
Group : SmallGroup(1728,21263)
Rank : 3
Schlafli Type : {6,48}
Number of vertices, edges, etc : 18, 432, 144
Order of s0s1s2 : 48
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,24}*864f
   3-fold quotients : {6,48}*576a, {6,48}*576b, {6,48}*576c
   4-fold quotients : {6,12}*432g
   6-fold quotients : {6,24}*288a, {6,24}*288b, {6,24}*288c
   8-fold quotients : {6,6}*216d
   9-fold quotients : {2,48}*192, {6,16}*192
   12-fold quotients : {6,12}*144a, {6,12}*144b, {6,12}*144c
   18-fold quotients : {2,24}*96, {6,8}*96
   24-fold quotients : {6,6}*72a, {6,6}*72b, {6,6}*72c
   27-fold quotients : {2,16}*64
   36-fold quotients : {2,12}*48, {6,4}*48a
   48-fold quotients : {3,6}*36, {6,3}*36
   54-fold quotients : {2,8}*32
   72-fold quotients : {2,6}*24, {6,2}*24
   108-fold quotients : {2,4}*16
   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> of order 3.
      96 facets:
         72 of {2}*4
         24 of {6}*12
      6 vertex figures:
         6 of {48}*96
   P/N, where N=<s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 3.
      48 facets:
         48 of {6}*12
      12 vertex figures:
         3 of {48}*96
         9 of {16}*32

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

Twisty Puzzle