Polytope of Type {20,46}

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

Twisty Puzzle