Polytope of Type {10,92}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle