Polytope of Type {24,3}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,3}*1152b
if this polytope has a name.
Group : SmallGroup(1152,157458)
Rank : 3
Schlafli Type : {24,3}
Number of vertices, edges, etc : 192, 288, 24
Order of s0s1s2 : 12
Order of s0s1s2s1 : 24
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 : {12,3}*576
   4-fold quotients : {24,3}*288
   8-fold quotients : {6,3}*144, {12,3}*144
   12-fold quotients : {8,3}*96
   24-fold quotients : {4,3}*48, {6,3}*48
   32-fold quotients : {6,3}*36
   48-fold quotients : {3,3}*24, {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=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1> of order 2.
      12 facets:
         12 of {24}*48
      96 vertex figures:
         96 of {3}*6
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2> of order 2.
      12 facets:
         12 of {24}*48
      96 vertex figures:
         96 of {3}*6
   P/N, where N=<s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2> of order 2.
      12 facets:
         12 of {24}*48
      96 vertex figures:
         96 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1> of order 3.
      12 facets:
         6 of {8}*16
         6 of {24}*48
      64 vertex figures:
         64 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2> of order 3.
      8 facets:
         8 of {24}*48
      64 vertex figures:
         64 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1, s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1> of order 4.
      6 facets:
         6 of {24}*48
      48 vertex figures:
         48 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2> of order 4.
      6 facets:
         6 of {24}*48
      48 vertex figures:
         48 of {3}*6
   P/N, where N=<s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1> of order 4.
      6 facets:
         6 of {24}*48
      48 vertex figures:
         48 of {3}*6
   P/N, where N=<s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1> of order 6.
      4 facets:
         4 of {24}*48
      32 vertex figures:
         32 of {3}*6

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

Twisty Puzzle