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}*1152i
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 : {12,24}*576c, {24,12}*576e
   3-fold quotients : {8,24}*384a, {24,8}*384d
   4-fold quotients : {6,24}*288a, {12,12}*288a
   6-fold quotients : {4,24}*192a, {24,4}*192b, {12,8}*192a, {8,12}*192b
   8-fold quotients : {6,12}*144a, {12,6}*144a
   9-fold quotients : {8,8}*128a
   12-fold quotients : {4,12}*96a, {12,4}*96a, {2,24}*96, {6,8}*96
   16-fold quotients : {6,6}*72a
   18-fold quotients : {4,8}*64a, {8,4}*64b
   24-fold quotients : {2,12}*48, {12,2}*48, {4,6}*48a, {6,4}*48a
   36-fold quotients : {4,4}*32, {2,8}*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 := (  1,433)(  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);;
s1 := (  1,  4)(  2,  6)(  3,  5)(  8,  9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)( 35, 36)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 52)( 44, 54)( 45, 53)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 70)( 62, 72)( 63, 71)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 97)( 80, 99)( 81, 98)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)( 88,106)( 89,108)( 90,107)(109,139)(110,141)(111,140)(112,136)(113,138)(114,137)(115,142)(116,144)(117,143)(118,130)(119,132)(120,131)(121,127)(122,129)(123,128)(124,133)(125,135)(126,134)(145,184)(146,186)(147,185)(148,181)(149,183)(150,182)(151,187)(152,189)(153,188)(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,196)(161,198)(162,197)(163,202)(164,204)(165,203)(166,199)(167,201)(168,200)(169,205)(170,207)(171,206)(172,211)(173,213)(174,212)(175,208)(176,210)(177,209)(178,214)(179,216)(180,215)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,277)(224,279)(225,278)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)(232,286)(233,288)(234,287)(235,256)(236,258)(237,257)(238,253)(239,255)(240,254)(241,259)(242,261)(243,260)(244,265)(245,267)(246,266)(247,262)(248,264)(249,263)(250,268)(251,270)(252,269)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)(297,368)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,376)(305,378)(306,377)(307,382)(308,384)(309,383)(310,379)(311,381)(312,380)(313,385)(314,387)(315,386)(316,391)(317,393)(318,392)(319,388)(320,390)(321,389)(322,394)(323,396)(324,395)(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)(331,412)(332,414)(333,413)(334,400)(335,402)(336,401)(337,397)(338,399)(339,398)(340,403)(341,405)(342,404)(343,427)(344,429)(345,428)(346,424)(347,426)(348,425)(349,430)(350,432)(351,431)(352,418)(353,420)(354,419)(355,415)(356,417)(357,416)(358,421)(359,423)(360,422)(433,553)(434,555)(435,554)(436,550)(437,552)(438,551)(439,556)(440,558)(441,557)(442,544)(443,546)(444,545)(445,541)(446,543)(447,542)(448,547)(449,549)(450,548)(451,571)(452,573)(453,572)(454,568)(455,570)(456,569)(457,574)(458,576)(459,575)(460,562)(461,564)(462,563)(463,559)(464,561)(465,560)(466,565)(467,567)(468,566)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,520)(476,522)(477,521)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,511)(485,513)(486,512)(487,535)(488,537)(489,536)(490,532)(491,534)(492,533)(493,538)(494,540)(495,539)(496,526)(497,528)(498,527)(499,523)(500,525)(501,524)(502,529)(503,531)(504,530);;
s2 := (  1,293)(  2,295)(  3,291)(  4,296)(  5,289)(  6,294)(  7,290)(  8,292)(  9,297)( 10,302)( 11,304)( 12,300)( 13,305)( 14,298)( 15,303)( 16,299)( 17,301)( 18,306)( 19,311)( 20,313)( 21,309)( 22,314)( 23,307)( 24,312)( 25,308)( 26,310)( 27,315)( 28,320)( 29,322)( 30,318)( 31,323)( 32,316)( 33,321)( 34,317)( 35,319)( 36,324)( 37,338)( 38,340)( 39,336)( 40,341)( 41,334)( 42,339)( 43,335)( 44,337)( 45,342)( 46,329)( 47,331)( 48,327)( 49,332)( 50,325)( 51,330)( 52,326)( 53,328)( 54,333)( 55,356)( 56,358)( 57,354)( 58,359)( 59,352)( 60,357)( 61,353)( 62,355)( 63,360)( 64,347)( 65,349)( 66,345)( 67,350)( 68,343)( 69,348)( 70,344)( 71,346)( 72,351)( 73,383)( 74,385)( 75,381)( 76,386)( 77,379)( 78,384)( 79,380)( 80,382)( 81,387)( 82,392)( 83,394)( 84,390)( 85,395)( 86,388)( 87,393)( 88,389)( 89,391)( 90,396)( 91,365)( 92,367)( 93,363)( 94,368)( 95,361)( 96,366)( 97,362)( 98,364)( 99,369)(100,374)(101,376)(102,372)(103,377)(104,370)(105,375)(106,371)(107,373)(108,378)(109,428)(110,430)(111,426)(112,431)(113,424)(114,429)(115,425)(116,427)(117,432)(118,419)(119,421)(120,417)(121,422)(122,415)(123,420)(124,416)(125,418)(126,423)(127,410)(128,412)(129,408)(130,413)(131,406)(132,411)(133,407)(134,409)(135,414)(136,401)(137,403)(138,399)(139,404)(140,397)(141,402)(142,398)(143,400)(144,405)(145,437)(146,439)(147,435)(148,440)(149,433)(150,438)(151,434)(152,436)(153,441)(154,446)(155,448)(156,444)(157,449)(158,442)(159,447)(160,443)(161,445)(162,450)(163,455)(164,457)(165,453)(166,458)(167,451)(168,456)(169,452)(170,454)(171,459)(172,464)(173,466)(174,462)(175,467)(176,460)(177,465)(178,461)(179,463)(180,468)(181,482)(182,484)(183,480)(184,485)(185,478)(186,483)(187,479)(188,481)(189,486)(190,473)(191,475)(192,471)(193,476)(194,469)(195,474)(196,470)(197,472)(198,477)(199,500)(200,502)(201,498)(202,503)(203,496)(204,501)(205,497)(206,499)(207,504)(208,491)(209,493)(210,489)(211,494)(212,487)(213,492)(214,488)(215,490)(216,495)(217,527)(218,529)(219,525)(220,530)(221,523)(222,528)(223,524)(224,526)(225,531)(226,536)(227,538)(228,534)(229,539)(230,532)(231,537)(232,533)(233,535)(234,540)(235,509)(236,511)(237,507)(238,512)(239,505)(240,510)(241,506)(242,508)(243,513)(244,518)(245,520)(246,516)(247,521)(248,514)(249,519)(250,515)(251,517)(252,522)(253,572)(254,574)(255,570)(256,575)(257,568)(258,573)(259,569)(260,571)(261,576)(262,563)(263,565)(264,561)(265,566)(266,559)(267,564)(268,560)(269,562)(270,567)(271,554)(272,556)(273,552)(274,557)(275,550)(276,555)(277,551)(278,553)(279,558)(280,545)(281,547)(282,543)(283,548)(284,541)(285,546)(286,542)(287,544)(288,549);;
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, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := 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);
s1 := Sym(576)!(  1,  4)(  2,  6)(  3,  5)(  8,  9)( 10, 13)( 11, 15)( 12, 14)( 17, 18)( 19, 22)( 20, 24)( 21, 23)( 26, 27)( 28, 31)( 29, 33)( 30, 32)( 35, 36)( 37, 49)( 38, 51)( 39, 50)( 40, 46)( 41, 48)( 42, 47)( 43, 52)( 44, 54)( 45, 53)( 55, 67)( 56, 69)( 57, 68)( 58, 64)( 59, 66)( 60, 65)( 61, 70)( 62, 72)( 63, 71)( 73, 94)( 74, 96)( 75, 95)( 76, 91)( 77, 93)( 78, 92)( 79, 97)( 80, 99)( 81, 98)( 82,103)( 83,105)( 84,104)( 85,100)( 86,102)( 87,101)( 88,106)( 89,108)( 90,107)(109,139)(110,141)(111,140)(112,136)(113,138)(114,137)(115,142)(116,144)(117,143)(118,130)(119,132)(120,131)(121,127)(122,129)(123,128)(124,133)(125,135)(126,134)(145,184)(146,186)(147,185)(148,181)(149,183)(150,182)(151,187)(152,189)(153,188)(154,193)(155,195)(156,194)(157,190)(158,192)(159,191)(160,196)(161,198)(162,197)(163,202)(164,204)(165,203)(166,199)(167,201)(168,200)(169,205)(170,207)(171,206)(172,211)(173,213)(174,212)(175,208)(176,210)(177,209)(178,214)(179,216)(180,215)(217,274)(218,276)(219,275)(220,271)(221,273)(222,272)(223,277)(224,279)(225,278)(226,283)(227,285)(228,284)(229,280)(230,282)(231,281)(232,286)(233,288)(234,287)(235,256)(236,258)(237,257)(238,253)(239,255)(240,254)(241,259)(242,261)(243,260)(244,265)(245,267)(246,266)(247,262)(248,264)(249,263)(250,268)(251,270)(252,269)(289,364)(290,366)(291,365)(292,361)(293,363)(294,362)(295,367)(296,369)(297,368)(298,373)(299,375)(300,374)(301,370)(302,372)(303,371)(304,376)(305,378)(306,377)(307,382)(308,384)(309,383)(310,379)(311,381)(312,380)(313,385)(314,387)(315,386)(316,391)(317,393)(318,392)(319,388)(320,390)(321,389)(322,394)(323,396)(324,395)(325,409)(326,411)(327,410)(328,406)(329,408)(330,407)(331,412)(332,414)(333,413)(334,400)(335,402)(336,401)(337,397)(338,399)(339,398)(340,403)(341,405)(342,404)(343,427)(344,429)(345,428)(346,424)(347,426)(348,425)(349,430)(350,432)(351,431)(352,418)(353,420)(354,419)(355,415)(356,417)(357,416)(358,421)(359,423)(360,422)(433,553)(434,555)(435,554)(436,550)(437,552)(438,551)(439,556)(440,558)(441,557)(442,544)(443,546)(444,545)(445,541)(446,543)(447,542)(448,547)(449,549)(450,548)(451,571)(452,573)(453,572)(454,568)(455,570)(456,569)(457,574)(458,576)(459,575)(460,562)(461,564)(462,563)(463,559)(464,561)(465,560)(466,565)(467,567)(468,566)(469,517)(470,519)(471,518)(472,514)(473,516)(474,515)(475,520)(476,522)(477,521)(478,508)(479,510)(480,509)(481,505)(482,507)(483,506)(484,511)(485,513)(486,512)(487,535)(488,537)(489,536)(490,532)(491,534)(492,533)(493,538)(494,540)(495,539)(496,526)(497,528)(498,527)(499,523)(500,525)(501,524)(502,529)(503,531)(504,530);
s2 := Sym(576)!(  1,293)(  2,295)(  3,291)(  4,296)(  5,289)(  6,294)(  7,290)(  8,292)(  9,297)( 10,302)( 11,304)( 12,300)( 13,305)( 14,298)( 15,303)( 16,299)( 17,301)( 18,306)( 19,311)( 20,313)( 21,309)( 22,314)( 23,307)( 24,312)( 25,308)( 26,310)( 27,315)( 28,320)( 29,322)( 30,318)( 31,323)( 32,316)( 33,321)( 34,317)( 35,319)( 36,324)( 37,338)( 38,340)( 39,336)( 40,341)( 41,334)( 42,339)( 43,335)( 44,337)( 45,342)( 46,329)( 47,331)( 48,327)( 49,332)( 50,325)( 51,330)( 52,326)( 53,328)( 54,333)( 55,356)( 56,358)( 57,354)( 58,359)( 59,352)( 60,357)( 61,353)( 62,355)( 63,360)( 64,347)( 65,349)( 66,345)( 67,350)( 68,343)( 69,348)( 70,344)( 71,346)( 72,351)( 73,383)( 74,385)( 75,381)( 76,386)( 77,379)( 78,384)( 79,380)( 80,382)( 81,387)( 82,392)( 83,394)( 84,390)( 85,395)( 86,388)( 87,393)( 88,389)( 89,391)( 90,396)( 91,365)( 92,367)( 93,363)( 94,368)( 95,361)( 96,366)( 97,362)( 98,364)( 99,369)(100,374)(101,376)(102,372)(103,377)(104,370)(105,375)(106,371)(107,373)(108,378)(109,428)(110,430)(111,426)(112,431)(113,424)(114,429)(115,425)(116,427)(117,432)(118,419)(119,421)(120,417)(121,422)(122,415)(123,420)(124,416)(125,418)(126,423)(127,410)(128,412)(129,408)(130,413)(131,406)(132,411)(133,407)(134,409)(135,414)(136,401)(137,403)(138,399)(139,404)(140,397)(141,402)(142,398)(143,400)(144,405)(145,437)(146,439)(147,435)(148,440)(149,433)(150,438)(151,434)(152,436)(153,441)(154,446)(155,448)(156,444)(157,449)(158,442)(159,447)(160,443)(161,445)(162,450)(163,455)(164,457)(165,453)(166,458)(167,451)(168,456)(169,452)(170,454)(171,459)(172,464)(173,466)(174,462)(175,467)(176,460)(177,465)(178,461)(179,463)(180,468)(181,482)(182,484)(183,480)(184,485)(185,478)(186,483)(187,479)(188,481)(189,486)(190,473)(191,475)(192,471)(193,476)(194,469)(195,474)(196,470)(197,472)(198,477)(199,500)(200,502)(201,498)(202,503)(203,496)(204,501)(205,497)(206,499)(207,504)(208,491)(209,493)(210,489)(211,494)(212,487)(213,492)(214,488)(215,490)(216,495)(217,527)(218,529)(219,525)(220,530)(221,523)(222,528)(223,524)(224,526)(225,531)(226,536)(227,538)(228,534)(229,539)(230,532)(231,537)(232,533)(233,535)(234,540)(235,509)(236,511)(237,507)(238,512)(239,505)(240,510)(241,506)(242,508)(243,513)(244,518)(245,520)(246,516)(247,521)(248,514)(249,519)(250,515)(251,517)(252,522)(253,572)(254,574)(255,570)(256,575)(257,568)(258,573)(259,569)(260,571)(261,576)(262,563)(263,565)(264,561)(265,566)(266,559)(267,564)(268,560)(269,562)(270,567)(271,554)(272,556)(273,552)(274,557)(275,550)(276,555)(277,551)(278,553)(279,558)(280,545)(281,547)(282,543)(283,548)(284,541)(285,546)(286,542)(287,544)(288,549);
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, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s1*s0, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >;
References : None.
to this polytope

Twisty Puzzle