Polytope of Type {4,144}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {4,144}*1152d
if this polytope has a name.
Group : SmallGroup(1152,154003)
Rank : 3
Schlafli Type : {4,144}
Number of vertices, edges, etc : 4, 288, 144
Order of s0s1s2 : 144
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
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 : {4,72}*576c
   3-fold quotients : {4,48}*384d
   4-fold quotients : {4,36}*288b
   6-fold quotients : {4,24}*192c
   8-fold quotients : {4,18}*144b
   12-fold quotients : {4,12}*96b
   16-fold quotients : {4,9}*72
   24-fold quotients : {4,6}*48c
   48-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle