Polytope of Type {18,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,8}*1152e
if this polytope has a name.
Group : SmallGroup(1152,154283)
Rank : 3
Schlafli Type : {18,8}
Number of vertices, edges, etc : 72, 288, 32
Order of s0s1s2 : 18
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {9,8}*576
   3-fold quotients : {6,8}*384e
   4-fold quotients : {18,4}*288
   6-fold quotients : {3,8}*192
   8-fold quotients : {9,4}*144, {18,4}*144b, {18,4}*144c
   12-fold quotients : {6,4}*96
   16-fold quotients : {9,4}*72, {18,2}*72
   24-fold quotients : {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {9,2}*36
   48-fold quotients : {3,4}*24, {6,2}*24
   96-fold quotients : {3,2}*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=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1> of order 2.
      16 facets:
         16 of {18}*36
      48 vertex figures:
         24 of {8}*16
         24 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 2.
      16 facets:
         16 of {18}*36
      36 vertex figures:
         36 of {8}*16
   P/N, where N=<s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 2.
      16 facets:
         16 of {18}*36
      36 vertex figures:
         36 of {8}*16
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {18}*36
      24 vertex figures:
         12 of {8}*16
         12 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 4.
      8 facets:
         8 of {18}*36
      36 vertex figures:
         12 of {8}*16
         24 of {2}*4
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 4.
      8 facets:
         8 of {18}*36
      24 vertex figures:
         12 of {8}*16
         12 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s2*s1, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 4.
      8 facets:
         8 of {18}*36
      24 vertex figures:
         12 of {8}*16
         12 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1, s0*s2*s1*s2*s1*s0*s2*s1*s2*s1*s2> of order 4.
      8 facets:
         8 of {18}*36
      24 vertex figures:
         12 of {8}*16
         12 of {4}*8

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