Polytope of Type {4,18}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,18}*1152a
if this polytope has a name.
Group : SmallGroup(1152,154282)
Rank : 3
Schlafli Type : {4,18}
Number of vertices, edges, etc : 32, 288, 144
Order of s0s1s2 : 18
Order of s0s1s2s1 : 4
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 : {4,18}*576a
   3-fold quotients : {4,6}*384a
   4-fold quotients : {4,18}*288
   6-fold quotients : {4,6}*192a
   8-fold quotients : {4,9}*144, {4,18}*144b, {4,18}*144c
   12-fold quotients : {4,6}*96
   16-fold quotients : {4,9}*72, {2,18}*72
   24-fold quotients : {4,3}*48, {4,6}*48b, {4,6}*48c
   32-fold quotients : {2,9}*36
   48-fold quotients : {4,3}*24, {2,6}*24
   96-fold quotients : {2,3}*12
   144-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*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2> of order 2.
      72 facets:
         72 of {4}*8
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 2.
      72 facets:
         72 of {4}*8
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 2.
      72 facets:
         72 of {4}*8
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      72 facets:
         72 of {4}*8
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      72 facets:
         72 of {4}*8
      20 vertex figures:
         8 of {9}*18
         12 of {18}*36
   P/N, where N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 2.
      84 facets:
         60 of {4}*8
         24 of {2}*4
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 2.
      72 facets:
         72 of {4}*8
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1> of order 2.
      72 facets:
         72 of {4}*8
      16 vertex figures:
         16 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      42 facets:
         30 of {4}*8
         12 of {2}*4
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      48 facets:
         24 of {2}*4
         24 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      48 facets:
         24 of {4}*8
         24 of {2}*4
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s1*s2, s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      54 facets:
         18 of {4}*8
         36 of {2}*4
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      36 facets:
         36 of {4}*8
      10 vertex figures:
         4 of {9}*18
         6 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      42 facets:
         30 of {4}*8
         12 of {2}*4
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      42 facets:
         30 of {4}*8
         12 of {2}*4
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 4.
      36 facets:
         36 of {4}*8
      12 vertex figures:
         8 of {9}*18
         4 of {18}*36
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1> of order 4.
      36 facets:
         36 of {4}*8
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 4.
      42 facets:
         30 of {4}*8
         12 of {2}*4
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 4.
      42 facets:
         30 of {4}*8
         12 of {2}*4
      8 vertex figures:
         8 of {18}*36
   P/N, where N=<s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 8.
      24 facets:
         12 of {4}*8
         12 of {2}*4
      4 vertex figures:
         4 of {18}*36
   P/N, where N=<s0*s1*s0*s1, s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 8.
      30 facets:
         24 of {2}*4
         6 of {4}*8
      4 vertex figures:
         4 of {18}*36
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 8.
      21 facets:
         15 of {4}*8
         6 of {2}*4
      4 vertex figures:
         4 of {18}*36
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2, s1*s0*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, s0*s2*s1*s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 8.
      18 facets:
         18 of {4}*8
      4 vertex figures:
         4 of {18}*36
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2> of order 8.
      24 facets:
         12 of {2}*4
         12 of {4}*8
      4 vertex figures:
         4 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 8.
      18 facets:
         18 of {4}*8
      4 vertex figures:
         4 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 8.
      18 facets:
         18 of {4}*8
      6 vertex figures:
         4 of {9}*18
         2 of {18}*36
   P/N, where N=<s0*s1*s0*s1, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 8.
      24 facets:
         12 of {2}*4
         12 of {4}*8
      6 vertex figures:
         4 of {9}*18
         2 of {18}*36
   P/N, where N=<s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2, s0*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2*s1*s2> of order 8.
      18 facets:
         18 of {4}*8
      4 vertex figures:
         4 of {18}*36
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s2, s0*s1*s0*s2*s1*s0*s1*s2*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 8.
      18 facets:
         18 of {4}*8
      4 vertex figures:
         4 of {18}*36
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2, s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 8.
      18 facets:
         18 of {4}*8
      6 vertex figures:
         4 of {9}*18
         2 of {18}*36
   P/N, where N=<s0*s1*s0*s1, s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 8.
      24 facets:
         12 of {2}*4
         12 of {4}*8
      4 vertex figures:
         4 of {18}*36

Permutation Representation (GAP) : 
s0 := (  1,297)(  2,298)(  3,299)(  4,300)(  5,301)(  6,302)(  7,303)(  8,304)(  9,289)( 10,290)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,296)( 17,313)( 18,314)( 19,315)( 20,316)( 21,317)( 22,318)( 23,319)( 24,320)( 25,305)( 26,306)( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)( 33,329)( 34,330)( 35,331)( 36,332)( 37,333)( 38,334)( 39,335)( 40,336)( 41,321)( 42,322)( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)( 48,328)( 49,345)( 50,346)( 51,347)( 52,348)( 53,349)( 54,350)( 55,351)( 56,352)( 57,337)( 58,338)( 59,339)( 60,340)( 61,341)( 62,342)( 63,343)( 64,344)( 65,361)( 66,362)( 67,363)( 68,364)( 69,365)( 70,366)( 71,367)( 72,368)( 73,353)( 74,354)( 75,355)( 76,356)( 77,357)( 78,358)( 79,359)( 80,360)( 81,377)( 82,378)( 83,379)( 84,380)( 85,381)( 86,382)( 87,383)( 88,384)( 89,369)( 90,370)( 91,371)( 92,372)( 93,373)( 94,374)( 95,375)( 96,376)( 97,393)( 98,394)( 99,395)(100,396)(101,397)(102,398)(103,399)(104,400)(105,385)(106,386)(107,387)(108,388)(109,389)(110,390)(111,391)(112,392)(113,409)(114,410)(115,411)(116,412)(117,413)(118,414)(119,415)(120,416)(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)(128,408)(129,425)(130,426)(131,427)(132,428)(133,429)(134,430)(135,431)(136,432)(137,417)(138,418)(139,419)(140,420)(141,421)(142,422)(143,423)(144,424)(145,441)(146,442)(147,443)(148,444)(149,445)(150,446)(151,447)(152,448)(153,433)(154,434)(155,435)(156,436)(157,437)(158,438)(159,439)(160,440)(161,457)(162,458)(163,459)(164,460)(165,461)(166,462)(167,463)(168,464)(169,449)(170,450)(171,451)(172,452)(173,453)(174,454)(175,455)(176,456)(177,473)(178,474)(179,475)(180,476)(181,477)(182,478)(183,479)(184,480)(185,465)(186,466)(187,467)(188,468)(189,469)(190,470)(191,471)(192,472)(193,489)(194,490)(195,491)(196,492)(197,493)(198,494)(199,495)(200,496)(201,481)(202,482)(203,483)(204,484)(205,485)(206,486)(207,487)(208,488)(209,505)(210,506)(211,507)(212,508)(213,509)(214,510)(215,511)(216,512)(217,497)(218,498)(219,499)(220,500)(221,501)(222,502)(223,503)(224,504)(225,521)(226,522)(227,523)(228,524)(229,525)(230,526)(231,527)(232,528)(233,513)(234,514)(235,515)(236,516)(237,517)(238,518)(239,519)(240,520)(241,537)(242,538)(243,539)(244,540)(245,541)(246,542)(247,543)(248,544)(249,529)(250,530)(251,531)(252,532)(253,533)(254,534)(255,535)(256,536)(257,553)(258,554)(259,555)(260,556)(261,557)(262,558)(263,559)(264,560)(265,545)(266,546)(267,547)(268,548)(269,549)(270,550)(271,551)(272,552)(273,569)(274,570)(275,571)(276,572)(277,573)(278,574)(279,575)(280,576)(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)(288,568);;
s1 := (  1,145)(  2,146)(  3,148)(  4,147)(  5,150)(  6,149)(  7,151)(  8,152)(  9,160)( 10,159)( 11,157)( 12,158)( 13,155)( 14,156)( 15,154)( 16,153)( 17,177)( 18,178)( 19,180)( 20,179)( 21,182)( 22,181)( 23,183)( 24,184)( 25,192)( 26,191)( 27,189)( 28,190)( 29,187)( 30,188)( 31,186)( 32,185)( 33,161)( 34,162)( 35,164)( 36,163)( 37,166)( 38,165)( 39,167)( 40,168)( 41,176)( 42,175)( 43,173)( 44,174)( 45,171)( 46,172)( 47,170)( 48,169)( 49,273)( 50,274)( 51,276)( 52,275)( 53,278)( 54,277)( 55,279)( 56,280)( 57,288)( 58,287)( 59,285)( 60,286)( 61,283)( 62,284)( 63,282)( 64,281)( 65,257)( 66,258)( 67,260)( 68,259)( 69,262)( 70,261)( 71,263)( 72,264)( 73,272)( 74,271)( 75,269)( 76,270)( 77,267)( 78,268)( 79,266)( 80,265)( 81,241)( 82,242)( 83,244)( 84,243)( 85,246)( 86,245)( 87,247)( 88,248)( 89,256)( 90,255)( 91,253)( 92,254)( 93,251)( 94,252)( 95,250)( 96,249)( 97,225)( 98,226)( 99,228)(100,227)(101,230)(102,229)(103,231)(104,232)(105,240)(106,239)(107,237)(108,238)(109,235)(110,236)(111,234)(112,233)(113,209)(114,210)(115,212)(116,211)(117,214)(118,213)(119,215)(120,216)(121,224)(122,223)(123,221)(124,222)(125,219)(126,220)(127,218)(128,217)(129,193)(130,194)(131,196)(132,195)(133,198)(134,197)(135,199)(136,200)(137,208)(138,207)(139,205)(140,206)(141,203)(142,204)(143,202)(144,201)(289,433)(290,434)(291,436)(292,435)(293,438)(294,437)(295,439)(296,440)(297,448)(298,447)(299,445)(300,446)(301,443)(302,444)(303,442)(304,441)(305,465)(306,466)(307,468)(308,467)(309,470)(310,469)(311,471)(312,472)(313,480)(314,479)(315,477)(316,478)(317,475)(318,476)(319,474)(320,473)(321,449)(322,450)(323,452)(324,451)(325,454)(326,453)(327,455)(328,456)(329,464)(330,463)(331,461)(332,462)(333,459)(334,460)(335,458)(336,457)(337,561)(338,562)(339,564)(340,563)(341,566)(342,565)(343,567)(344,568)(345,576)(346,575)(347,573)(348,574)(349,571)(350,572)(351,570)(352,569)(353,545)(354,546)(355,548)(356,547)(357,550)(358,549)(359,551)(360,552)(361,560)(362,559)(363,557)(364,558)(365,555)(366,556)(367,554)(368,553)(369,529)(370,530)(371,532)(372,531)(373,534)(374,533)(375,535)(376,536)(377,544)(378,543)(379,541)(380,542)(381,539)(382,540)(383,538)(384,537)(385,513)(386,514)(387,516)(388,515)(389,518)(390,517)(391,519)(392,520)(393,528)(394,527)(395,525)(396,526)(397,523)(398,524)(399,522)(400,521)(401,497)(402,498)(403,500)(404,499)(405,502)(406,501)(407,503)(408,504)(409,512)(410,511)(411,509)(412,510)(413,507)(414,508)(415,506)(416,505)(417,481)(418,482)(419,484)(420,483)(421,486)(422,485)(423,487)(424,488)(425,496)(426,495)(427,493)(428,494)(429,491)(430,492)(431,490)(432,489);;
s2 := (  1, 49)(  2, 52)(  3, 51)(  4, 50)(  5, 61)(  6, 64)(  7, 63)(  8, 62)(  9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 77)( 38, 80)( 39, 79)( 40, 78)( 41, 73)( 42, 76)( 43, 75)( 44, 74)( 45, 69)( 46, 72)( 47, 71)( 48, 70)( 97,129)( 98,132)( 99,131)(100,130)(101,141)(102,144)(103,143)(104,142)(105,137)(106,140)(107,139)(108,138)(109,133)(110,136)(111,135)(112,134)(114,116)(117,125)(118,128)(119,127)(120,126)(122,124)(145,193)(146,196)(147,195)(148,194)(149,205)(150,208)(151,207)(152,206)(153,201)(154,204)(155,203)(156,202)(157,197)(158,200)(159,199)(160,198)(161,225)(162,228)(163,227)(164,226)(165,237)(166,240)(167,239)(168,238)(169,233)(170,236)(171,235)(172,234)(173,229)(174,232)(175,231)(176,230)(177,209)(178,212)(179,211)(180,210)(181,221)(182,224)(183,223)(184,222)(185,217)(186,220)(187,219)(188,218)(189,213)(190,216)(191,215)(192,214)(241,273)(242,276)(243,275)(244,274)(245,285)(246,288)(247,287)(248,286)(249,281)(250,284)(251,283)(252,282)(253,277)(254,280)(255,279)(256,278)(258,260)(261,269)(262,272)(263,271)(264,270)(266,268)(289,337)(290,340)(291,339)(292,338)(293,349)(294,352)(295,351)(296,350)(297,345)(298,348)(299,347)(300,346)(301,341)(302,344)(303,343)(304,342)(305,369)(306,372)(307,371)(308,370)(309,381)(310,384)(311,383)(312,382)(313,377)(314,380)(315,379)(316,378)(317,373)(318,376)(319,375)(320,374)(321,353)(322,356)(323,355)(324,354)(325,365)(326,368)(327,367)(328,366)(329,361)(330,364)(331,363)(332,362)(333,357)(334,360)(335,359)(336,358)(385,417)(386,420)(387,419)(388,418)(389,429)(390,432)(391,431)(392,430)(393,425)(394,428)(395,427)(396,426)(397,421)(398,424)(399,423)(400,422)(402,404)(405,413)(406,416)(407,415)(408,414)(410,412)(433,481)(434,484)(435,483)(436,482)(437,493)(438,496)(439,495)(440,494)(441,489)(442,492)(443,491)(444,490)(445,485)(446,488)(447,487)(448,486)(449,513)(450,516)(451,515)(452,514)(453,525)(454,528)(455,527)(456,526)(457,521)(458,524)(459,523)(460,522)(461,517)(462,520)(463,519)(464,518)(465,497)(466,500)(467,499)(468,498)(469,509)(470,512)(471,511)(472,510)(473,505)(474,508)(475,507)(476,506)(477,501)(478,504)(479,503)(480,502)(529,561)(530,564)(531,563)(532,562)(533,573)(534,576)(535,575)(536,574)(537,569)(538,572)(539,571)(540,570)(541,565)(542,568)(543,567)(544,566)(546,548)(549,557)(550,560)(551,559)(552,558)(554,556);;
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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*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 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(576)!(  1,297)(  2,298)(  3,299)(  4,300)(  5,301)(  6,302)(  7,303)(  8,304)(  9,289)( 10,290)( 11,291)( 12,292)( 13,293)( 14,294)( 15,295)( 16,296)( 17,313)( 18,314)( 19,315)( 20,316)( 21,317)( 22,318)( 23,319)( 24,320)( 25,305)( 26,306)( 27,307)( 28,308)( 29,309)( 30,310)( 31,311)( 32,312)( 33,329)( 34,330)( 35,331)( 36,332)( 37,333)( 38,334)( 39,335)( 40,336)( 41,321)( 42,322)( 43,323)( 44,324)( 45,325)( 46,326)( 47,327)( 48,328)( 49,345)( 50,346)( 51,347)( 52,348)( 53,349)( 54,350)( 55,351)( 56,352)( 57,337)( 58,338)( 59,339)( 60,340)( 61,341)( 62,342)( 63,343)( 64,344)( 65,361)( 66,362)( 67,363)( 68,364)( 69,365)( 70,366)( 71,367)( 72,368)( 73,353)( 74,354)( 75,355)( 76,356)( 77,357)( 78,358)( 79,359)( 80,360)( 81,377)( 82,378)( 83,379)( 84,380)( 85,381)( 86,382)( 87,383)( 88,384)( 89,369)( 90,370)( 91,371)( 92,372)( 93,373)( 94,374)( 95,375)( 96,376)( 97,393)( 98,394)( 99,395)(100,396)(101,397)(102,398)(103,399)(104,400)(105,385)(106,386)(107,387)(108,388)(109,389)(110,390)(111,391)(112,392)(113,409)(114,410)(115,411)(116,412)(117,413)(118,414)(119,415)(120,416)(121,401)(122,402)(123,403)(124,404)(125,405)(126,406)(127,407)(128,408)(129,425)(130,426)(131,427)(132,428)(133,429)(134,430)(135,431)(136,432)(137,417)(138,418)(139,419)(140,420)(141,421)(142,422)(143,423)(144,424)(145,441)(146,442)(147,443)(148,444)(149,445)(150,446)(151,447)(152,448)(153,433)(154,434)(155,435)(156,436)(157,437)(158,438)(159,439)(160,440)(161,457)(162,458)(163,459)(164,460)(165,461)(166,462)(167,463)(168,464)(169,449)(170,450)(171,451)(172,452)(173,453)(174,454)(175,455)(176,456)(177,473)(178,474)(179,475)(180,476)(181,477)(182,478)(183,479)(184,480)(185,465)(186,466)(187,467)(188,468)(189,469)(190,470)(191,471)(192,472)(193,489)(194,490)(195,491)(196,492)(197,493)(198,494)(199,495)(200,496)(201,481)(202,482)(203,483)(204,484)(205,485)(206,486)(207,487)(208,488)(209,505)(210,506)(211,507)(212,508)(213,509)(214,510)(215,511)(216,512)(217,497)(218,498)(219,499)(220,500)(221,501)(222,502)(223,503)(224,504)(225,521)(226,522)(227,523)(228,524)(229,525)(230,526)(231,527)(232,528)(233,513)(234,514)(235,515)(236,516)(237,517)(238,518)(239,519)(240,520)(241,537)(242,538)(243,539)(244,540)(245,541)(246,542)(247,543)(248,544)(249,529)(250,530)(251,531)(252,532)(253,533)(254,534)(255,535)(256,536)(257,553)(258,554)(259,555)(260,556)(261,557)(262,558)(263,559)(264,560)(265,545)(266,546)(267,547)(268,548)(269,549)(270,550)(271,551)(272,552)(273,569)(274,570)(275,571)(276,572)(277,573)(278,574)(279,575)(280,576)(281,561)(282,562)(283,563)(284,564)(285,565)(286,566)(287,567)(288,568);
s1 := Sym(576)!(  1,145)(  2,146)(  3,148)(  4,147)(  5,150)(  6,149)(  7,151)(  8,152)(  9,160)( 10,159)( 11,157)( 12,158)( 13,155)( 14,156)( 15,154)( 16,153)( 17,177)( 18,178)( 19,180)( 20,179)( 21,182)( 22,181)( 23,183)( 24,184)( 25,192)( 26,191)( 27,189)( 28,190)( 29,187)( 30,188)( 31,186)( 32,185)( 33,161)( 34,162)( 35,164)( 36,163)( 37,166)( 38,165)( 39,167)( 40,168)( 41,176)( 42,175)( 43,173)( 44,174)( 45,171)( 46,172)( 47,170)( 48,169)( 49,273)( 50,274)( 51,276)( 52,275)( 53,278)( 54,277)( 55,279)( 56,280)( 57,288)( 58,287)( 59,285)( 60,286)( 61,283)( 62,284)( 63,282)( 64,281)( 65,257)( 66,258)( 67,260)( 68,259)( 69,262)( 70,261)( 71,263)( 72,264)( 73,272)( 74,271)( 75,269)( 76,270)( 77,267)( 78,268)( 79,266)( 80,265)( 81,241)( 82,242)( 83,244)( 84,243)( 85,246)( 86,245)( 87,247)( 88,248)( 89,256)( 90,255)( 91,253)( 92,254)( 93,251)( 94,252)( 95,250)( 96,249)( 97,225)( 98,226)( 99,228)(100,227)(101,230)(102,229)(103,231)(104,232)(105,240)(106,239)(107,237)(108,238)(109,235)(110,236)(111,234)(112,233)(113,209)(114,210)(115,212)(116,211)(117,214)(118,213)(119,215)(120,216)(121,224)(122,223)(123,221)(124,222)(125,219)(126,220)(127,218)(128,217)(129,193)(130,194)(131,196)(132,195)(133,198)(134,197)(135,199)(136,200)(137,208)(138,207)(139,205)(140,206)(141,203)(142,204)(143,202)(144,201)(289,433)(290,434)(291,436)(292,435)(293,438)(294,437)(295,439)(296,440)(297,448)(298,447)(299,445)(300,446)(301,443)(302,444)(303,442)(304,441)(305,465)(306,466)(307,468)(308,467)(309,470)(310,469)(311,471)(312,472)(313,480)(314,479)(315,477)(316,478)(317,475)(318,476)(319,474)(320,473)(321,449)(322,450)(323,452)(324,451)(325,454)(326,453)(327,455)(328,456)(329,464)(330,463)(331,461)(332,462)(333,459)(334,460)(335,458)(336,457)(337,561)(338,562)(339,564)(340,563)(341,566)(342,565)(343,567)(344,568)(345,576)(346,575)(347,573)(348,574)(349,571)(350,572)(351,570)(352,569)(353,545)(354,546)(355,548)(356,547)(357,550)(358,549)(359,551)(360,552)(361,560)(362,559)(363,557)(364,558)(365,555)(366,556)(367,554)(368,553)(369,529)(370,530)(371,532)(372,531)(373,534)(374,533)(375,535)(376,536)(377,544)(378,543)(379,541)(380,542)(381,539)(382,540)(383,538)(384,537)(385,513)(386,514)(387,516)(388,515)(389,518)(390,517)(391,519)(392,520)(393,528)(394,527)(395,525)(396,526)(397,523)(398,524)(399,522)(400,521)(401,497)(402,498)(403,500)(404,499)(405,502)(406,501)(407,503)(408,504)(409,512)(410,511)(411,509)(412,510)(413,507)(414,508)(415,506)(416,505)(417,481)(418,482)(419,484)(420,483)(421,486)(422,485)(423,487)(424,488)(425,496)(426,495)(427,493)(428,494)(429,491)(430,492)(431,490)(432,489);
s2 := Sym(576)!(  1, 49)(  2, 52)(  3, 51)(  4, 50)(  5, 61)(  6, 64)(  7, 63)(  8, 62)(  9, 57)( 10, 60)( 11, 59)( 12, 58)( 13, 53)( 14, 56)( 15, 55)( 16, 54)( 17, 81)( 18, 84)( 19, 83)( 20, 82)( 21, 93)( 22, 96)( 23, 95)( 24, 94)( 25, 89)( 26, 92)( 27, 91)( 28, 90)( 29, 85)( 30, 88)( 31, 87)( 32, 86)( 33, 65)( 34, 68)( 35, 67)( 36, 66)( 37, 77)( 38, 80)( 39, 79)( 40, 78)( 41, 73)( 42, 76)( 43, 75)( 44, 74)( 45, 69)( 46, 72)( 47, 71)( 48, 70)( 97,129)( 98,132)( 99,131)(100,130)(101,141)(102,144)(103,143)(104,142)(105,137)(106,140)(107,139)(108,138)(109,133)(110,136)(111,135)(112,134)(114,116)(117,125)(118,128)(119,127)(120,126)(122,124)(145,193)(146,196)(147,195)(148,194)(149,205)(150,208)(151,207)(152,206)(153,201)(154,204)(155,203)(156,202)(157,197)(158,200)(159,199)(160,198)(161,225)(162,228)(163,227)(164,226)(165,237)(166,240)(167,239)(168,238)(169,233)(170,236)(171,235)(172,234)(173,229)(174,232)(175,231)(176,230)(177,209)(178,212)(179,211)(180,210)(181,221)(182,224)(183,223)(184,222)(185,217)(186,220)(187,219)(188,218)(189,213)(190,216)(191,215)(192,214)(241,273)(242,276)(243,275)(244,274)(245,285)(246,288)(247,287)(248,286)(249,281)(250,284)(251,283)(252,282)(253,277)(254,280)(255,279)(256,278)(258,260)(261,269)(262,272)(263,271)(264,270)(266,268)(289,337)(290,340)(291,339)(292,338)(293,349)(294,352)(295,351)(296,350)(297,345)(298,348)(299,347)(300,346)(301,341)(302,344)(303,343)(304,342)(305,369)(306,372)(307,371)(308,370)(309,381)(310,384)(311,383)(312,382)(313,377)(314,380)(315,379)(316,378)(317,373)(318,376)(319,375)(320,374)(321,353)(322,356)(323,355)(324,354)(325,365)(326,368)(327,367)(328,366)(329,361)(330,364)(331,363)(332,362)(333,357)(334,360)(335,359)(336,358)(385,417)(386,420)(387,419)(388,418)(389,429)(390,432)(391,431)(392,430)(393,425)(394,428)(395,427)(396,426)(397,421)(398,424)(399,423)(400,422)(402,404)(405,413)(406,416)(407,415)(408,414)(410,412)(433,481)(434,484)(435,483)(436,482)(437,493)(438,496)(439,495)(440,494)(441,489)(442,492)(443,491)(444,490)(445,485)(446,488)(447,487)(448,486)(449,513)(450,516)(451,515)(452,514)(453,525)(454,528)(455,527)(456,526)(457,521)(458,524)(459,523)(460,522)(461,517)(462,520)(463,519)(464,518)(465,497)(466,500)(467,499)(468,498)(469,509)(470,512)(471,511)(472,510)(473,505)(474,508)(475,507)(476,506)(477,501)(478,504)(479,503)(480,502)(529,561)(530,564)(531,563)(532,562)(533,573)(534,576)(535,575)(536,574)(537,569)(538,572)(539,571)(540,570)(541,565)(542,568)(543,567)(544,566)(546,548)(549,557)(550,560)(551,559)(552,558)(554,556);
poly := sub<Sym(576)|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*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s2*s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*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 >;
References : None.
to this polytope

Twisty Puzzle