Polytope of Type {24,24}

Play with this polytope as a twisty puzzle

s0 := (  1,289)(  2,291)(  3,290)(  4,295)(  5,297)(  6,296)(  7,292)(  8,294)(  9,293)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)( 16,301)( 17,303)( 18,302)( 19,307)( 20,309)( 21,308)( 22,313)( 23,315)( 24,314)( 25,310)( 26,312)( 27,311)( 28,316)( 29,318)( 30,317)( 31,322)( 32,324)( 33,323)( 34,319)( 35,321)( 36,320)( 37,334)( 38,336)( 39,335)( 40,340)( 41,342)( 42,341)( 43,337)( 44,339)( 45,338)( 46,325)( 47,327)( 48,326)( 49,331)( 50,333)( 51,332)( 52,328)( 53,330)( 54,329)( 55,352)( 56,354)( 57,353)( 58,358)( 59,360)( 60,359)( 61,355)( 62,357)( 63,356)( 64,343)( 65,345)( 66,344)( 67,349)( 68,351)( 69,350)( 70,346)( 71,348)( 72,347)( 73,379)( 74,381)( 75,380)( 76,385)( 77,387)( 78,386)( 79,382)( 80,384)( 81,383)( 82,388)( 83,390)( 84,389)( 85,394)( 86,396)( 87,395)( 88,391)( 89,393)( 90,392)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)( 96,368)( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)(104,378)(105,377)(106,373)(107,375)(108,374)(109,424)(110,426)(111,425)(112,430)(113,432)(114,431)(115,427)(116,429)(117,428)(118,415)(119,417)(120,416)(121,421)(122,423)(123,422)(124,418)(125,420)(126,419)(127,406)(128,408)(129,407)(130,412)(131,414)(132,413)(133,409)(134,411)(135,410)(136,397)(137,399)(138,398)(139,403)(140,405)(141,404)(142,400)(143,402)(144,401)(145,433)(146,435)(147,434)(148,439)(149,441)(150,440)(151,436)(152,438)(153,437)(154,442)(155,444)(156,443)(157,448)(158,450)(159,449)(160,445)(161,447)(162,446)(163,451)(164,453)(165,452)(166,457)(167,459)(168,458)(169,454)(170,456)(171,455)(172,460)(173,462)(174,461)(175,466)(176,468)(177,467)(178,463)(179,465)(180,464)(181,478)(182,480)(183,479)(184,484)(185,486)(186,485)(187,481)(188,483)(189,482)(190,469)(191,471)(192,470)(193,475)(194,477)(195,476)(196,472)(197,474)(198,473)(199,496)(200,498)(201,497)(202,502)(203,504)(204,503)(205,499)(206,501)(207,500)(208,487)(209,489)(210,488)(211,493)(212,495)(213,494)(214,490)(215,492)(216,491)(217,523)(218,525)(219,524)(220,529)(221,531)(222,530)(223,526)(224,528)(225,527)(226,532)(227,534)(228,533)(229,538)(230,540)(231,539)(232,535)(233,537)(234,536)(235,505)(236,507)(237,506)(238,511)(239,513)(240,512)(241,508)(242,510)(243,509)(244,514)(245,516)(246,515)(247,520)(248,522)(249,521)(250,517)(251,519)(252,518)(253,568)(254,570)(255,569)(256,574)(257,576)(258,575)(259,571)(260,573)(261,572)(262,559)(263,561)(264,560)(265,565)(266,567)(267,566)(268,562)(269,564)(270,563)(271,550)(272,552)(273,551)(274,556)(275,558)(276,557)(277,553)(278,555)(279,554)(280,541)(281,543)(282,542)(283,547)(284,549)(285,548)(286,544)(287,546)(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 := (  1,145)(  2,150)(  3,152)(  4,148)(  5,153)(  6,146)(  7,151)(  8,147)(  9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,190)( 38,195)( 39,197)( 40,193)( 41,198)( 42,191)( 43,196)( 44,192)( 45,194)( 46,181)( 47,186)( 48,188)( 49,184)( 50,189)( 51,182)( 52,187)( 53,183)( 54,185)( 55,208)( 56,213)( 57,215)( 58,211)( 59,216)( 60,209)( 61,214)( 62,210)( 63,212)( 64,199)( 65,204)( 66,206)( 67,202)( 68,207)( 69,200)( 70,205)( 71,201)( 72,203)( 73,226)( 74,231)( 75,233)( 76,229)( 77,234)( 78,227)( 79,232)( 80,228)( 81,230)( 82,217)( 83,222)( 84,224)( 85,220)( 86,225)( 87,218)( 88,223)( 89,219)( 90,221)( 91,244)( 92,249)( 93,251)( 94,247)( 95,252)( 96,245)( 97,250)( 98,246)( 99,248)(100,235)(101,240)(102,242)(103,238)(104,243)(105,236)(106,241)(107,237)(108,239)(109,253)(110,258)(111,260)(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)(321,461)(322,466)(323,462)(324,464)(325,478)(326,483)(327,485)(328,481)(329,486)(330,479)(331,484)(332,480)(333,482)(334,469)(335,474)(336,476)(337,472)(338,477)(339,470)(340,475)(341,471)(342,473)(343,496)(344,501)(345,503)(346,499)(347,504)(348,497)(349,502)(350,498)(351,500)(352,487)(353,492)(354,494)(355,490)(356,495)(357,488)(358,493)(359,489)(360,491)(361,514)(362,519)(363,521)(364,517)(365,522)(366,515)(367,520)(368,516)(369,518)(370,505)(371,510)(372,512)(373,508)(374,513)(375,506)(376,511)(377,507)(378,509)(379,532)(380,537)(381,539)(382,535)(383,540)(384,533)(385,538)(386,534)(387,536)(388,523)(389,528)(390,530)(391,526)(392,531)(393,524)(394,529)(395,525)(396,527)(397,541)(398,546)(399,548)(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);;
poly := Group([s0,s1,s2]);;
 

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, s2*s0*s1*s2*s1*s2*s0*s1*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, 
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
 

s0 := Sym(576)!(  1,289)(  2,291)(  3,290)(  4,295)(  5,297)(  6,296)(  7,292)(  8,294)(  9,293)( 10,298)( 11,300)( 12,299)( 13,304)( 14,306)( 15,305)( 16,301)( 17,303)( 18,302)( 19,307)( 20,309)( 21,308)( 22,313)( 23,315)( 24,314)( 25,310)( 26,312)( 27,311)( 28,316)( 29,318)( 30,317)( 31,322)( 32,324)( 33,323)( 34,319)( 35,321)( 36,320)( 37,334)( 38,336)( 39,335)( 40,340)( 41,342)( 42,341)( 43,337)( 44,339)( 45,338)( 46,325)( 47,327)( 48,326)( 49,331)( 50,333)( 51,332)( 52,328)( 53,330)( 54,329)( 55,352)( 56,354)( 57,353)( 58,358)( 59,360)( 60,359)( 61,355)( 62,357)( 63,356)( 64,343)( 65,345)( 66,344)( 67,349)( 68,351)( 69,350)( 70,346)( 71,348)( 72,347)( 73,379)( 74,381)( 75,380)( 76,385)( 77,387)( 78,386)( 79,382)( 80,384)( 81,383)( 82,388)( 83,390)( 84,389)( 85,394)( 86,396)( 87,395)( 88,391)( 89,393)( 90,392)( 91,361)( 92,363)( 93,362)( 94,367)( 95,369)( 96,368)( 97,364)( 98,366)( 99,365)(100,370)(101,372)(102,371)(103,376)(104,378)(105,377)(106,373)(107,375)(108,374)(109,424)(110,426)(111,425)(112,430)(113,432)(114,431)(115,427)(116,429)(117,428)(118,415)(119,417)(120,416)(121,421)(122,423)(123,422)(124,418)(125,420)(126,419)(127,406)(128,408)(129,407)(130,412)(131,414)(132,413)(133,409)(134,411)(135,410)(136,397)(137,399)(138,398)(139,403)(140,405)(141,404)(142,400)(143,402)(144,401)(145,433)(146,435)(147,434)(148,439)(149,441)(150,440)(151,436)(152,438)(153,437)(154,442)(155,444)(156,443)(157,448)(158,450)(159,449)(160,445)(161,447)(162,446)(163,451)(164,453)(165,452)(166,457)(167,459)(168,458)(169,454)(170,456)(171,455)(172,460)(173,462)(174,461)(175,466)(176,468)(177,467)(178,463)(179,465)(180,464)(181,478)(182,480)(183,479)(184,484)(185,486)(186,485)(187,481)(188,483)(189,482)(190,469)(191,471)(192,470)(193,475)(194,477)(195,476)(196,472)(197,474)(198,473)(199,496)(200,498)(201,497)(202,502)(203,504)(204,503)(205,499)(206,501)(207,500)(208,487)(209,489)(210,488)(211,493)(212,495)(213,494)(214,490)(215,492)(216,491)(217,523)(218,525)(219,524)(220,529)(221,531)(222,530)(223,526)(224,528)(225,527)(226,532)(227,534)(228,533)(229,538)(230,540)(231,539)(232,535)(233,537)(234,536)(235,505)(236,507)(237,506)(238,511)(239,513)(240,512)(241,508)(242,510)(243,509)(244,514)(245,516)(246,515)(247,520)(248,522)(249,521)(250,517)(251,519)(252,518)(253,568)(254,570)(255,569)(256,574)(257,576)(258,575)(259,571)(260,573)(261,572)(262,559)(263,561)(264,560)(265,565)(266,567)(267,566)(268,562)(269,564)(270,563)(271,550)(272,552)(273,551)(274,556)(275,558)(276,557)(277,553)(278,555)(279,554)(280,541)(281,543)(282,542)(283,547)(284,549)(285,548)(286,544)(287,546)(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)!(  1,145)(  2,150)(  3,152)(  4,148)(  5,153)(  6,146)(  7,151)(  8,147)(  9,149)( 10,154)( 11,159)( 12,161)( 13,157)( 14,162)( 15,155)( 16,160)( 17,156)( 18,158)( 19,163)( 20,168)( 21,170)( 22,166)( 23,171)( 24,164)( 25,169)( 26,165)( 27,167)( 28,172)( 29,177)( 30,179)( 31,175)( 32,180)( 33,173)( 34,178)( 35,174)( 36,176)( 37,190)( 38,195)( 39,197)( 40,193)( 41,198)( 42,191)( 43,196)( 44,192)( 45,194)( 46,181)( 47,186)( 48,188)( 49,184)( 50,189)( 51,182)( 52,187)( 53,183)( 54,185)( 55,208)( 56,213)( 57,215)( 58,211)( 59,216)( 60,209)( 61,214)( 62,210)( 63,212)( 64,199)( 65,204)( 66,206)( 67,202)( 68,207)( 69,200)( 70,205)( 71,201)( 72,203)( 73,226)( 74,231)( 75,233)( 76,229)( 77,234)( 78,227)( 79,232)( 80,228)( 81,230)( 82,217)( 83,222)( 84,224)( 85,220)( 86,225)( 87,218)( 88,223)( 89,219)( 90,221)( 91,244)( 92,249)( 93,251)( 94,247)( 95,252)( 96,245)( 97,250)( 98,246)( 99,248)(100,235)(101,240)(102,242)(103,238)(104,243)(105,236)(106,241)(107,237)(108,239)(109,253)(110,258)(111,260)(112,256)(113,261)(114,254)(115,259)(116,255)(117,257)(118,262)(119,267)(120,269)(121,265)(122,270)(123,263)(124,268)(125,264)(126,266)(127,271)(128,276)(129,278)(130,274)(131,279)(132,272)(133,277)(134,273)(135,275)(136,280)(137,285)(138,287)(139,283)(140,288)(141,281)(142,286)(143,282)(144,284)(289,433)(290,438)(291,440)(292,436)(293,441)(294,434)(295,439)(296,435)(297,437)(298,442)(299,447)(300,449)(301,445)(302,450)(303,443)(304,448)(305,444)(306,446)(307,451)(308,456)(309,458)(310,454)(311,459)(312,452)(313,457)(314,453)(315,455)(316,460)(317,465)(318,467)(319,463)(320,468)(321,461)(322,466)(323,462)(324,464)(325,478)(326,483)(327,485)(328,481)(329,486)(330,479)(331,484)(332,480)(333,482)(334,469)(335,474)(336,476)(337,472)(338,477)(339,470)(340,475)(341,471)(342,473)(343,496)(344,501)(345,503)(346,499)(347,504)(348,497)(349,502)(350,498)(351,500)(352,487)(353,492)(354,494)(355,490)(356,495)(357,488)(358,493)(359,489)(360,491)(361,514)(362,519)(363,521)(364,517)(365,522)(366,515)(367,520)(368,516)(369,518)(370,505)(371,510)(372,512)(373,508)(374,513)(375,506)(376,511)(377,507)(378,509)(379,532)(380,537)(381,539)(382,535)(383,540)(384,533)(385,538)(386,534)(387,536)(388,523)(389,528)(390,530)(391,526)(392,531)(393,524)(394,529)(395,525)(396,527)(397,541)(398,546)(399,548)(400,544)(401,549)(402,542)(403,547)(404,543)(405,545)(406,550)(407,555)(408,557)(409,553)(410,558)(411,551)(412,556)(413,552)(414,554)(415,559)(416,564)(417,566)(418,562)(419,567)(420,560)(421,565)(422,561)(423,563)(424,568)(425,573)(426,575)(427,571)(428,576)(429,569)(430,574)(431,570)(432,572);
poly := sub<Sym(576)|s0,s1,s2>;
 

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s2*s0*s1*s2*s1*s2*s0*s1*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, 
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >; 
 

Twisty Puzzle