Polytope of Type {24,24}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {24,24}*1152g
if this polytope has a name.
Group : SmallGroup(1152,12917)
Rank : 3
Schlafli Type : {24,24}
Number of vertices, edges, etc : 24, 288, 24
Order of s0s1s2 : 24
Order of s0s1s2s1 : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
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 : {24,12}*576c, {12,24}*576e
   3-fold quotients : {24,8}*384a, {8,24}*384d
   4-fold quotients : {24,6}*288a, {12,12}*288a
   6-fold quotients : {24,4}*192a, {4,24}*192b, {8,12}*192a, {12,8}*192b
   8-fold quotients : {6,12}*144a, {12,6}*144a
   9-fold quotients : {8,8}*128c
   12-fold quotients : {4,12}*96a, {12,4}*96a, {24,2}*96, {8,6}*96
   16-fold quotients : {6,6}*72a
   18-fold quotients : {8,4}*64a, {4,8}*64b
   24-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
   36-fold quotients : {4,4}*32, {8,2}*32
   48-fold quotients : {2,6}*24, {6,2}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {2,3}*12, {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle