Polytope of Type {6,150}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle