Polytope of Type {72,4}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {72,4}*1152c
if this polytope has a name.
Group : SmallGroup(1152,154349)
Rank : 3
Schlafli Type : {72,4}
Number of vertices, edges, etc : 144, 288, 8
Order of s0s1s2 : 72
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Self-Petrie
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 : {72,4}*576c, {72,4}*576d, {36,4}*576b
   3-fold quotients : {24,4}*384c
   4-fold quotients : {72,2}*288, {36,4}*288b, {36,4}*288c, {18,4}*288
   6-fold quotients : {24,4}*192c, {24,4}*192d, {12,4}*192b
   8-fold quotients : {36,2}*144, {9,4}*144, {18,4}*144b, {18,4}*144c
   12-fold quotients : {24,2}*96, {12,4}*96b, {12,4}*96c, {6,4}*96
   16-fold quotients : {9,4}*72, {18,2}*72
   24-fold quotients : {12,2}*48, {3,4}*48, {6,4}*48b, {6,4}*48c
   32-fold quotients : {9,2}*36
   36-fold quotients : {8,2}*32
   48-fold quotients : {3,4}*24, {6,2}*24
   72-fold quotients : {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):
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1> of order 2.
      4 facets:
         4 of {72}*144
      96 vertex figures:
         48 of {4}*8
         48 of {2}*4

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

Twisty Puzzle