Polytope of Type {8,18}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle