Polytope of Type {72,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {72,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,12900)
Rank : 3
Schlafli Type : {72,8}
Number of vertices, edges, etc : 72, 288, 8
Order of s0s1s2 : 72
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
   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 : {72,4}*576b, {36,8}*576a
   3-fold quotients : {24,8}*384d
   4-fold quotients : {36,4}*288a, {18,8}*288
   6-fold quotients : {24,4}*192b, {12,8}*192a
   8-fold quotients : {36,2}*144, {18,4}*144a
   9-fold quotients : {8,8}*128a
   12-fold quotients : {12,4}*96a, {6,8}*96
   16-fold quotients : {18,2}*72
   18-fold quotients : {4,8}*64a, {8,4}*64b
   24-fold quotients : {12,2}*48, {6,4}*48a
   32-fold quotients : {9,2}*36
   36-fold quotients : {4,4}*32, {2,8}*32
   48-fold quotients : {6,2}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {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)(  2,147)(  3,146)(  4,153)(  5,152)(  6,151)(  7,150)(  8,149)(  9,148)( 10,154)( 11,156)( 12,155)( 13,162)( 14,161)( 15,160)( 16,159)( 17,158)( 18,157)( 19,163)( 20,165)( 21,164)( 22,171)( 23,170)( 24,169)( 25,168)( 26,167)( 27,166)( 28,172)( 29,174)( 30,173)( 31,180)( 32,179)( 33,178)( 34,177)( 35,176)( 36,175)( 37,190)( 38,192)( 39,191)( 40,198)( 41,197)( 42,196)( 43,195)( 44,194)( 45,193)( 46,181)( 47,183)( 48,182)( 49,189)( 50,188)( 51,187)( 52,186)( 53,185)( 54,184)( 55,208)( 56,210)( 57,209)( 58,216)( 59,215)( 60,214)( 61,213)( 62,212)( 63,211)( 64,199)( 65,201)( 66,200)( 67,207)( 68,206)( 69,205)( 70,204)( 71,203)( 72,202)( 73,226)( 74,228)( 75,227)( 76,234)( 77,233)( 78,232)( 79,231)( 80,230)( 81,229)( 82,217)( 83,219)( 84,218)( 85,225)( 86,224)( 87,223)( 88,222)( 89,221)( 90,220)( 91,244)( 92,246)( 93,245)( 94,252)( 95,251)( 96,250)( 97,249)( 98,248)( 99,247)(100,235)(101,237)(102,236)(103,243)(104,242)(105,241)(106,240)(107,239)(108,238)(109,253)(110,255)(111,254)(112,261)(113,260)(114,259)(115,258)(116,257)(117,256)(118,262)(119,264)(120,263)(121,270)(122,269)(123,268)(124,267)(125,266)(126,265)(127,271)(128,273)(129,272)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)(136,280)(137,282)(138,281)(139,288)(140,287)(141,286)(142,285)(143,284)(144,283)(289,433)(290,435)(291,434)(292,441)(293,440)(294,439)(295,438)(296,437)(297,436)(298,442)(299,444)(300,443)(301,450)(302,449)(303,448)(304,447)(305,446)(306,445)(307,451)(308,453)(309,452)(310,459)(311,458)(312,457)(313,456)(314,455)(315,454)(316,460)(317,462)(318,461)(319,468)(320,467)(321,466)(322,465)(323,464)(324,463)(325,478)(326,480)(327,479)(328,486)(329,485)(330,484)(331,483)(332,482)(333,481)(334,469)(335,471)(336,470)(337,477)(338,476)(339,475)(340,474)(341,473)(342,472)(343,496)(344,498)(345,497)(346,504)(347,503)(348,502)(349,501)(350,500)(351,499)(352,487)(353,489)(354,488)(355,495)(356,494)(357,493)(358,492)(359,491)(360,490)(361,514)(362,516)(363,515)(364,522)(365,521)(366,520)(367,519)(368,518)(369,517)(370,505)(371,507)(372,506)(373,513)(374,512)(375,511)(376,510)(377,509)(378,508)(379,532)(380,534)(381,533)(382,540)(383,539)(384,538)(385,537)(386,536)(387,535)(388,523)(389,525)(390,524)(391,531)(392,530)(393,529)(394,528)(395,527)(396,526)(397,541)(398,543)(399,542)(400,549)(401,548)(402,547)(403,546)(404,545)(405,544)(406,550)(407,552)(408,551)(409,558)(410,557)(411,556)(412,555)(413,554)(414,553)(415,559)(416,561)(417,560)(418,567)(419,566)(420,565)(421,564)(422,563)(423,562)(424,568)(425,570)(426,569)(427,576)(428,575)(429,574)(430,573)(431,572)(432,571);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  7,  9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)( 19, 22)( 20, 24)( 21, 23)( 25, 27)( 28, 31)( 29, 33)( 30, 32)( 34, 36)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 54)( 44, 53)( 45, 52)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)( 62, 71)( 63, 70)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 99)( 80, 98)( 81, 97)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)( 88,108)( 89,107)( 90,106)(109,139)(110,141)(111,140)(112,136)(113,138)(114,137)(115,144)(116,143)(117,142)(118,130)(119,132)(120,131)(121,127)(122,129)(123,128)(124,135)(125,134)(126,133)(145,184)(146,186)(147,185)(148,181)(149,183)(150,182)(151,189)(152,188)(153,187)(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,198)(161,197)(162,196)(163,202)(164,204)(165,203)(166,199)(167,201)(168,200)(169,207)(170,206)(171,205)(172,211)(173,213)(174,212)(175,208)(176,210)(177,209)(178,216)(179,215)(180,214)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,279)(224,278)(225,277)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)(232,288)(233,287)(234,286)(235,256)(236,258)(237,257)(238,253)(239,255)(240,254)(241,261)(242,260)(243,259)(244,265)(245,267)(246,266)(247,262)(248,264)(249,263)(250,270)(251,269)(252,268)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,369)(296,368)(297,367)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,378)(305,377)(306,376)(307,382)(308,384)(309,383)(310,379)(311,381)(312,380)(313,387)(314,386)(315,385)(316,391)(317,393)(318,392)(319,388)(320,390)(321,389)(322,396)(323,395)(324,394)(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)(331,414)(332,413)(333,412)(334,400)(335,402)(336,401)(337,397)(338,399)(339,398)(340,405)(341,404)(342,403)(343,427)(344,429)(345,428)(346,424)(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)(354,419)(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(433,553)(434,555)(435,554)(436,550)(437,552)(438,551)(439,558)(440,557)(441,556)(442,544)(443,546)(444,545)(445,541)(446,543)(447,542)(448,549)(449,548)(450,547)(451,571)(452,573)(453,572)(454,568)(455,570)(456,569)(457,576)(458,575)(459,574)(460,562)(461,564)(462,563)(463,559)(464,561)(465,560)(466,567)(467,566)(468,565)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,522)(476,521)(477,520)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,513)(485,512)(486,511)(487,535)(488,537)(489,536)(490,532)(491,534)(492,533)(493,540)(494,539)(495,538)(496,526)(497,528)(498,527)(499,523)(500,525)(501,524)(502,531)(503,530)(504,529);;
s2 := (  1,289)(  2,290)(  3,291)(  4,292)(  5,293)(  6,294)(  7,295)(  8,296)(  9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)( 80,386)( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)( 88,394)( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)( 96,366)( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)(104,374)(105,375)(106,376)(107,377)(108,378)(109,424)(110,425)(111,426)(112,427)(113,428)(114,429)(115,430)(116,431)(117,432)(118,415)(119,416)(120,417)(121,418)(122,419)(123,420)(124,421)(125,422)(126,423)(127,406)(128,407)(129,408)(130,409)(131,410)(132,411)(133,412)(134,413)(135,414)(136,397)(137,398)(138,399)(139,400)(140,401)(141,402)(142,403)(143,404)(144,405)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)(161,449)(162,450)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,496)(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)(224,530)(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)(232,538)(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)(240,510)(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)(248,518)(249,519)(250,520)(251,521)(252,522)(253,568)(254,569)(255,570)(256,571)(257,572)(258,573)(259,574)(260,575)(261,576)(262,559)(263,560)(264,561)(265,562)(266,563)(267,564)(268,565)(269,566)(270,567)(271,550)(272,551)(273,552)(274,553)(275,554)(276,555)(277,556)(278,557)(279,558)(280,541)(281,542)(282,543)(283,544)(284,545)(285,546)(286,547)(287,548)(288,549);;
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*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s2*s1*s0*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(576)!(  1,145)(  2,147)(  3,146)(  4,153)(  5,152)(  6,151)(  7,150)(  8,149)(  9,148)( 10,154)( 11,156)( 12,155)( 13,162)( 14,161)( 15,160)( 16,159)( 17,158)( 18,157)( 19,163)( 20,165)( 21,164)( 22,171)( 23,170)( 24,169)( 25,168)( 26,167)( 27,166)( 28,172)( 29,174)( 30,173)( 31,180)( 32,179)( 33,178)( 34,177)( 35,176)( 36,175)( 37,190)( 38,192)( 39,191)( 40,198)( 41,197)( 42,196)( 43,195)( 44,194)( 45,193)( 46,181)( 47,183)( 48,182)( 49,189)( 50,188)( 51,187)( 52,186)( 53,185)( 54,184)( 55,208)( 56,210)( 57,209)( 58,216)( 59,215)( 60,214)( 61,213)( 62,212)( 63,211)( 64,199)( 65,201)( 66,200)( 67,207)( 68,206)( 69,205)( 70,204)( 71,203)( 72,202)( 73,226)( 74,228)( 75,227)( 76,234)( 77,233)( 78,232)( 79,231)( 80,230)( 81,229)( 82,217)( 83,219)( 84,218)( 85,225)( 86,224)( 87,223)( 88,222)( 89,221)( 90,220)( 91,244)( 92,246)( 93,245)( 94,252)( 95,251)( 96,250)( 97,249)( 98,248)( 99,247)(100,235)(101,237)(102,236)(103,243)(104,242)(105,241)(106,240)(107,239)(108,238)(109,253)(110,255)(111,254)(112,261)(113,260)(114,259)(115,258)(116,257)(117,256)(118,262)(119,264)(120,263)(121,270)(122,269)(123,268)(124,267)(125,266)(126,265)(127,271)(128,273)(129,272)(130,279)(131,278)(132,277)(133,276)(134,275)(135,274)(136,280)(137,282)(138,281)(139,288)(140,287)(141,286)(142,285)(143,284)(144,283)(289,433)(290,435)(291,434)(292,441)(293,440)(294,439)(295,438)(296,437)(297,436)(298,442)(299,444)(300,443)(301,450)(302,449)(303,448)(304,447)(305,446)(306,445)(307,451)(308,453)(309,452)(310,459)(311,458)(312,457)(313,456)(314,455)(315,454)(316,460)(317,462)(318,461)(319,468)(320,467)(321,466)(322,465)(323,464)(324,463)(325,478)(326,480)(327,479)(328,486)(329,485)(330,484)(331,483)(332,482)(333,481)(334,469)(335,471)(336,470)(337,477)(338,476)(339,475)(340,474)(341,473)(342,472)(343,496)(344,498)(345,497)(346,504)(347,503)(348,502)(349,501)(350,500)(351,499)(352,487)(353,489)(354,488)(355,495)(356,494)(357,493)(358,492)(359,491)(360,490)(361,514)(362,516)(363,515)(364,522)(365,521)(366,520)(367,519)(368,518)(369,517)(370,505)(371,507)(372,506)(373,513)(374,512)(375,511)(376,510)(377,509)(378,508)(379,532)(380,534)(381,533)(382,540)(383,539)(384,538)(385,537)(386,536)(387,535)(388,523)(389,525)(390,524)(391,531)(392,530)(393,529)(394,528)(395,527)(396,526)(397,541)(398,543)(399,542)(400,549)(401,548)(402,547)(403,546)(404,545)(405,544)(406,550)(407,552)(408,551)(409,558)(410,557)(411,556)(412,555)(413,554)(414,553)(415,559)(416,561)(417,560)(418,567)(419,566)(420,565)(421,564)(422,563)(423,562)(424,568)(425,570)(426,569)(427,576)(428,575)(429,574)(430,573)(431,572)(432,571);
s1 := Sym(576)!(  1,  4)(  2,  6)(  3,  5)(  7,  9)( 10, 13)( 11, 15)( 12, 14)( 16, 18)( 19, 22)( 20, 24)( 21, 23)( 25, 27)( 28, 31)( 29, 33)( 30, 32)( 34, 36)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 54)( 44, 53)( 45, 52)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 72)( 62, 71)( 63, 70)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 99)( 80, 98)( 81, 97)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)( 88,108)( 89,107)( 90,106)(109,139)(110,141)(111,140)(112,136)(113,138)(114,137)(115,144)(116,143)(117,142)(118,130)(119,132)(120,131)(121,127)(122,129)(123,128)(124,135)(125,134)(126,133)(145,184)(146,186)(147,185)(148,181)(149,183)(150,182)(151,189)(152,188)(153,187)(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,198)(161,197)(162,196)(163,202)(164,204)(165,203)(166,199)(167,201)(168,200)(169,207)(170,206)(171,205)(172,211)(173,213)(174,212)(175,208)(176,210)(177,209)(178,216)(179,215)(180,214)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,279)(224,278)(225,277)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)(232,288)(233,287)(234,286)(235,256)(236,258)(237,257)(238,253)(239,255)(240,254)(241,261)(242,260)(243,259)(244,265)(245,267)(246,266)(247,262)(248,264)(249,263)(250,270)(251,269)(252,268)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,369)(296,368)(297,367)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,378)(305,377)(306,376)(307,382)(308,384)(309,383)(310,379)(311,381)(312,380)(313,387)(314,386)(315,385)(316,391)(317,393)(318,392)(319,388)(320,390)(321,389)(322,396)(323,395)(324,394)(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)(331,414)(332,413)(333,412)(334,400)(335,402)(336,401)(337,397)(338,399)(339,398)(340,405)(341,404)(342,403)(343,427)(344,429)(345,428)(346,424)(347,426)(348,425)(349,432)(350,431)(351,430)(352,418)(353,420)(354,419)(355,415)(356,417)(357,416)(358,423)(359,422)(360,421)(433,553)(434,555)(435,554)(436,550)(437,552)(438,551)(439,558)(440,557)(441,556)(442,544)(443,546)(444,545)(445,541)(446,543)(447,542)(448,549)(449,548)(450,547)(451,571)(452,573)(453,572)(454,568)(455,570)(456,569)(457,576)(458,575)(459,574)(460,562)(461,564)(462,563)(463,559)(464,561)(465,560)(466,567)(467,566)(468,565)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,522)(476,521)(477,520)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,513)(485,512)(486,511)(487,535)(488,537)(489,536)(490,532)(491,534)(492,533)(493,540)(494,539)(495,538)(496,526)(497,528)(498,527)(499,523)(500,525)(501,524)(502,531)(503,530)(504,529);
s2 := Sym(576)!(  1,289)(  2,290)(  3,291)(  4,292)(  5,293)(  6,294)(  7,295)(  8,296)(  9,297)( 10,298)( 11,299)( 12,300)( 13,301)( 14,302)( 15,303)( 16,304)( 17,305)( 18,306)( 19,307)( 20,308)( 21,309)( 22,310)( 23,311)( 24,312)( 25,313)( 26,314)( 27,315)( 28,316)( 29,317)( 30,318)( 31,319)( 32,320)( 33,321)( 34,322)( 35,323)( 36,324)( 37,334)( 38,335)( 39,336)( 40,337)( 41,338)( 42,339)( 43,340)( 44,341)( 45,342)( 46,325)( 47,326)( 48,327)( 49,328)( 50,329)( 51,330)( 52,331)( 53,332)( 54,333)( 55,352)( 56,353)( 57,354)( 58,355)( 59,356)( 60,357)( 61,358)( 62,359)( 63,360)( 64,343)( 65,344)( 66,345)( 67,346)( 68,347)( 69,348)( 70,349)( 71,350)( 72,351)( 73,379)( 74,380)( 75,381)( 76,382)( 77,383)( 78,384)( 79,385)( 80,386)( 81,387)( 82,388)( 83,389)( 84,390)( 85,391)( 86,392)( 87,393)( 88,394)( 89,395)( 90,396)( 91,361)( 92,362)( 93,363)( 94,364)( 95,365)( 96,366)( 97,367)( 98,368)( 99,369)(100,370)(101,371)(102,372)(103,373)(104,374)(105,375)(106,376)(107,377)(108,378)(109,424)(110,425)(111,426)(112,427)(113,428)(114,429)(115,430)(116,431)(117,432)(118,415)(119,416)(120,417)(121,418)(122,419)(123,420)(124,421)(125,422)(126,423)(127,406)(128,407)(129,408)(130,409)(131,410)(132,411)(133,412)(134,413)(135,414)(136,397)(137,398)(138,399)(139,400)(140,401)(141,402)(142,403)(143,404)(144,405)(145,433)(146,434)(147,435)(148,436)(149,437)(150,438)(151,439)(152,440)(153,441)(154,442)(155,443)(156,444)(157,445)(158,446)(159,447)(160,448)(161,449)(162,450)(163,451)(164,452)(165,453)(166,454)(167,455)(168,456)(169,457)(170,458)(171,459)(172,460)(173,461)(174,462)(175,463)(176,464)(177,465)(178,466)(179,467)(180,468)(181,478)(182,479)(183,480)(184,481)(185,482)(186,483)(187,484)(188,485)(189,486)(190,469)(191,470)(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,496)(200,497)(201,498)(202,499)(203,500)(204,501)(205,502)(206,503)(207,504)(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)(217,523)(218,524)(219,525)(220,526)(221,527)(222,528)(223,529)(224,530)(225,531)(226,532)(227,533)(228,534)(229,535)(230,536)(231,537)(232,538)(233,539)(234,540)(235,505)(236,506)(237,507)(238,508)(239,509)(240,510)(241,511)(242,512)(243,513)(244,514)(245,515)(246,516)(247,517)(248,518)(249,519)(250,520)(251,521)(252,522)(253,568)(254,569)(255,570)(256,571)(257,572)(258,573)(259,574)(260,575)(261,576)(262,559)(263,560)(264,561)(265,562)(266,563)(267,564)(268,565)(269,566)(270,567)(271,550)(272,551)(273,552)(274,553)(275,554)(276,555)(277,556)(278,557)(279,558)(280,541)(281,542)(282,543)(283,544)(284,545)(285,546)(286,547)(287,548)(288,549);
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*s1*s0*s1*s0*s1*s0*s1*s2*s1, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
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*s2*s1*s0*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*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >;
References : None.
to this polytope

Twisty Puzzle