Polytope of Type {8,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,24}*1152c
if this polytope has a name.
Group : SmallGroup(1152,12921)
Rank : 3
Schlafli Type : {8,24}
Number of vertices, edges, etc : 24, 288, 72
Order of s0s1s2 : 8
Order of s0s1s2s1 : 6
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 : {8,12}*576a, {4,24}*576a
   4-fold quotients : {8,6}*288, {4,12}*288
   8-fold quotients : {4,6}*144
   9-fold quotients : {8,8}*128b
   16-fold quotients : {4,6}*72
   18-fold quotients : {4,8}*64a, {8,4}*64a
   36-fold quotients : {4,4}*32, {2,8}*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*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2> of order 3.
      24 facets:
         24 of {8}*16
      16 vertex figures:
         4 of {24}*48
         12 of {8}*16
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
      24 facets:
         24 of {8}*16
      8 vertex figures:
         8 of {24}*48

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

Twisty Puzzle