Polytope of Type {16,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {16,12}*1152a
if this polytope has a name.
Group : SmallGroup(1152,32085)
Rank : 3
Schlafli Type : {16,12}
Number of vertices, edges, etc : 48, 288, 36
Order of s0s1s2 : 16
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 : {16,6}*576, {8,12}*576a
   4-fold quotients : {8,6}*288, {4,12}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {16,4}*128a
   16-fold quotients : {4,6}*72
   18-fold quotients : {8,4}*64a, {16,2}*64
   36-fold quotients : {4,4}*32, {8,2}*32
   72-fold quotients : {2,4}*16, {4,2}*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*s2*s1*s2*s1*s2*s1*s0*s2> of order 3.
      12 facets:
         12 of {16}*32
      32 vertex figures:
         8 of {12}*24
         24 of {4}*8
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 3.
      12 facets:
         12 of {16}*32
      16 vertex figures:
         16 of {12}*24

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