Polytope of Type {6,32}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,32}*1152
if this polytope has a name.
Group : SmallGroup(1152,34520)
Rank : 3
Schlafli Type : {6,32}
Number of vertices, edges, etc : 18, 288, 96
Order of s0s1s2 : 32
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 : {6,16}*576
   4-fold quotients : {6,8}*288
   8-fold quotients : {6,4}*144
   9-fold quotients : {2,32}*128
   16-fold quotients : {6,4}*72
   18-fold quotients : {2,16}*64
   36-fold quotients : {2,8}*32
   72-fold quotients : {2,4}*16
   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*s0*s1> of order 3.
      64 facets:
         48 of {2}*4
         16 of {6}*12
      6 vertex figures:
         6 of {32}*64
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      32 facets:
         32 of {6}*12
      6 vertex figures:
         6 of {32}*64

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