Polytope of Type {24,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,24}*1152b
Also Known As : {24,24|2}. if this polytope has another name.
Group : SmallGroup(1152,12914)
Rank : 3
Schlafli Type : {24,24}
Number of vertices, edges, etc : 24, 288, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   Self-Dual
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 : {12,24}*576c, {24,12}*576c
   3-fold quotients : {8,24}*384b, {24,8}*384b
   4-fold quotients : {6,24}*288a, {24,6}*288a, {12,12}*288a
   6-fold quotients : {4,24}*192a, {24,4}*192a, {8,12}*192a, {12,8}*192a
   8-fold quotients : {6,12}*144a, {12,6}*144a
   9-fold quotients : {8,8}*128b
   12-fold quotients : {4,12}*96a, {12,4}*96a, {2,24}*96, {24,2}*96, {6,8}*96, {8,6}*96
   16-fold quotients : {6,6}*72a
   18-fold quotients : {4,8}*64a, {8,4}*64a
   24-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
   36-fold quotients : {4,4}*32, {2,8}*32, {8,2}*32
   48-fold quotients : {2,6}*24, {6,2}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {2,3}*12, {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):
   None.

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