Polytope of Type {12,16}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,16}*1152b
if this polytope has a name.
Group : SmallGroup(1152,32302)
Rank : 3
Schlafli Type : {12,16}
Number of vertices, edges, etc : 36, 288, 48
Order of s0s1s2 : 16
Order of s0s1s2s1 : 12
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,8}*576a
   4-fold quotients : {6,8}*288, {12,4}*288
   8-fold quotients : {6,4}*144
   9-fold quotients : {4,16}*128b
   16-fold quotients : {6,4}*72
   18-fold quotients : {4,8}*64a
   36-fold quotients : {4,4}*32, {2,8}*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*s0*s1> of order 3.
      32 facets:
         24 of {4}*8
         8 of {12}*24
      12 vertex figures:
         12 of {16}*32
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1> of order 3.
      16 facets:
         16 of {12}*24
      12 vertex figures:
         12 of {16}*32

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

Twisty Puzzle