Polytope of Type {8,8}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,8}*1152c
if this polytope has a name.
Group : SmallGroup(1152,12921)
Rank : 3
Schlafli Type : {8,8}
Number of vertices, edges, etc : 72, 288, 72
Order of s0s1s2 : 24
Order of s0s1s2s1 : 12
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 : {4,8}*576a, {8,4}*576b
   4-fold quotients : {4,4}*288
   8-fold quotients : {4,4}*144
   9-fold quotients : {8,8}*128a
   16-fold quotients : {4,4}*72
   18-fold quotients : {4,8}*64a, {8,4}*64b
   36-fold quotients : {4,4}*32, {2,8}*32
   72-fold quotients : {2,4}*16, {4,2}*16
   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*s0*s2*s1*s0*s1*s2*s1> of order 2.
      36 facets:
         36 of {8}*16
      36 vertex figures:
         36 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s2*s1*s0*s2*s1*s0*s1*s2*s1*s2> of order 3.
      24 facets:
         24 of {8}*16
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2> of order 3.
      24 facets:
         24 of {8}*16
      24 vertex figures:
         24 of {8}*16
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s2, s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s2*s1> of order 6.
      12 facets:
         12 of {8}*16
      12 vertex figures:
         12 of {8}*16

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

Twisty Puzzle