Polytope of Type {24,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,12}*1152c
if this polytope has a name.
Group : SmallGroup(1152,12014)
Rank : 3
Schlafli Type : {24,12}
Number of vertices, edges, etc : 48, 288, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
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 : {24,12}*576a, {12,12}*576b, {24,12}*576b
   3-fold quotients : {8,12}*384a
   4-fold quotients : {12,12}*288b, {24,6}*288c
   6-fold quotients : {4,12}*192a, {8,12}*192a, {8,12}*192b
   8-fold quotients : {6,12}*144b, {12,6}*144c
   9-fold quotients : {8,4}*128a
   12-fold quotients : {4,12}*96a, {8,6}*96
   16-fold quotients : {6,6}*72b
   18-fold quotients : {8,4}*64a, {8,4}*64b, {4,4}*64
   24-fold quotients : {2,12}*48, {4,6}*48a
   32-fold quotients : {6,3}*36
   36-fold quotients : {4,4}*32, {8,2}*32
   48-fold quotients : {2,6}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   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=<s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      12 facets:
         12 of {24}*48
      36 vertex figures:
         24 of {6}*12
         12 of {12}*24

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

Twisty Puzzle