Polytope of Type {4,238}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle