Polytope of Type {24,10}

Play with this polytope as a twisty puzzle

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

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

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

Twisty Puzzle