Polytope of Type {48,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {48,4}*1152a
if this polytope has a name.
Group : SmallGroup(1152,32083)
Rank : 3
Schlafli Type : {48,4}
Number of vertices, edges, etc : 144, 288, 12
Order of s0s1s2 : 16
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
   Skewing Operation
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {24,4}*576a
   4-fold quotients : {12,4}*288
   8-fold quotients : {6,4}*144
   9-fold quotients : {16,4}*128a
   16-fold quotients : {6,4}*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*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      6 facets:
         6 of {48}*96
      72 vertex figures:
         72 of {4}*8
   P/N, where N=<s1*s0*s1*s2*s1*s0*s1*s2> of order 3.
      4 facets:
         4 of {48}*96
      48 vertex figures:
         48 of {4}*8
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 3.
      8 facets:
         6 of {16}*32
         2 of {48}*96
      48 vertex figures:
         48 of {4}*8

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

Twisty Puzzle