Polytope of Type {50,18}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle