Polytope of Type {6,154}

Play with this polytope as a twisty puzzle

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

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

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

Twisty Puzzle