Polytope of Type {18,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {18,8}*1152a
if this polytope has a name.
Group : SmallGroup(1152,153963)
Rank : 3
Schlafli Type : {18,8}
Number of vertices, edges, etc : 72, 288, 32
Order of s0s1s2 : 36
Order of s0s1s2s1 : 8
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
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 : {9,8}*576
   3-fold quotients : {6,8}*384a
   6-fold quotients : {3,8}*192
   8-fold quotients : {9,4}*144
   16-fold quotients : {9,4}*72
   24-fold quotients : {3,4}*48
   32-fold quotients : {9,2}*36
   48-fold quotients : {3,4}*24
   96-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2> of order 2.
      16 facets:
         16 of {18}*36
      48 vertex figures:
         24 of {4}*8
         24 of {8}*16
   P/N, where N=<s1*s2*s1*s2*s1*s2*s1*s2, s0*s1*s0*s2*s1*s2*s1*s0*s2*s1*s0*s2> of order 4.
      8 facets:
         8 of {18}*36
      24 vertex figures:
         12 of {4}*8
         12 of {8}*16

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

Twisty Puzzle