Polytope of Type {48,6}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,6}*1728f
if this polytope has a name.
Group : SmallGroup(1728,21263)
Rank : 3
Schlafli Type : {48,6}
Number of vertices, edges, etc : 144, 432, 18
Order of s0s1s2 : 48
Order of s0s1s2s1 : 6
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 : {24,6}*864f
   3-fold quotients : {48,6}*576a, {48,6}*576b, {48,6}*576c
   4-fold quotients : {12,6}*432g
   6-fold quotients : {24,6}*288a, {24,6}*288b, {24,6}*288c
   8-fold quotients : {6,6}*216d
   9-fold quotients : {48,2}*192, {16,6}*192
   12-fold quotients : {12,6}*144a, {12,6}*144b, {12,6}*144c
   18-fold quotients : {24,2}*96, {8,6}*96
   24-fold quotients : {6,6}*72a, {6,6}*72b, {6,6}*72c
   27-fold quotients : {16,2}*64
   36-fold quotients : {12,2}*48, {4,6}*48a
   48-fold quotients : {3,6}*36, {6,3}*36
   54-fold quotients : {8,2}*32
   72-fold quotients : {2,6}*24, {6,2}*24
   108-fold quotients : {4,2}*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*s2*s1*s0*s2> of order 3.
      6 facets:
         6 of {48}*96
      96 vertex figures:
         24 of {6}*12
         72 of {2}*4
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      12 facets:
         9 of {16}*32
         3 of {48}*96
      48 vertex figures:
         48 of {6}*12

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

Twisty Puzzle