Polytope of Type {4,250}

Play with this polytope as a twisty puzzle

s0 := (251,376)(252,377)(253,378)(254,379)(255,380)(256,381)(257,382)(258,383)(259,384)(260,385)(261,386)(262,387)(263,388)(264,389)(265,390)(266,391)(267,392)(268,393)(269,394)(270,395)(271,396)(272,397)(273,398)(274,399)(275,400)(276,401)(277,402)(278,403)(279,404)(280,405)(281,406)(282,407)(283,408)(284,409)(285,410)(286,411)(287,412)(288,413)(289,414)(290,415)(291,416)(292,417)(293,418)(294,419)(295,420)(296,421)(297,422)(298,423)(299,424)(300,425)(301,426)(302,427)(303,428)(304,429)(305,430)(306,431)(307,432)(308,433)(309,434)(310,435)(311,436)(312,437)(313,438)(314,439)(315,440)(316,441)(317,442)(318,443)(319,444)(320,445)(321,446)(322,447)(323,448)(324,449)(325,450)(326,451)(327,452)(328,453)(329,454)(330,455)(331,456)(332,457)(333,458)(334,459)(335,460)(336,461)(337,462)(338,463)(339,464)(340,465)(341,466)(342,467)(343,468)(344,469)(345,470)(346,471)(347,472)(348,473)(349,474)(350,475)(351,476)(352,477)(353,478)(354,479)(355,480)(356,481)(357,482)(358,483)(359,484)(360,485)(361,486)(362,487)(363,488)(364,489)(365,490)(366,491)(367,492)(368,493)(369,494)(370,495)(371,496)(372,497)(373,498)(374,499)(375,500);;
s1 := (  1,251)(  2,255)(  3,254)(  4,253)(  5,252)(  6,275)(  7,274)(  8,273)(  9,272)( 10,271)( 11,270)( 12,269)( 13,268)( 14,267)( 15,266)( 16,265)( 17,264)( 18,263)( 19,262)( 20,261)( 21,260)( 22,259)( 23,258)( 24,257)( 25,256)( 26,375)( 27,374)( 28,373)( 29,372)( 30,371)( 31,370)( 32,369)( 33,368)( 34,367)( 35,366)( 36,365)( 37,364)( 38,363)( 39,362)( 40,361)( 41,360)( 42,359)( 43,358)( 44,357)( 45,356)( 46,355)( 47,354)( 48,353)( 49,352)( 50,351)( 51,350)( 52,349)( 53,348)( 54,347)( 55,346)( 56,345)( 57,344)( 58,343)( 59,342)( 60,341)( 61,340)( 62,339)( 63,338)( 64,337)( 65,336)( 66,335)( 67,334)( 68,333)( 69,332)( 70,331)( 71,330)( 72,329)( 73,328)( 74,327)( 75,326)( 76,325)( 77,324)( 78,323)( 79,322)( 80,321)( 81,320)( 82,319)( 83,318)( 84,317)( 85,316)( 86,315)( 87,314)( 88,313)( 89,312)( 90,311)( 91,310)( 92,309)( 93,308)( 94,307)( 95,306)( 96,305)( 97,304)( 98,303)( 99,302)(100,301)(101,300)(102,299)(103,298)(104,297)(105,296)(106,295)(107,294)(108,293)(109,292)(110,291)(111,290)(112,289)(113,288)(114,287)(115,286)(116,285)(117,284)(118,283)(119,282)(120,281)(121,280)(122,279)(123,278)(124,277)(125,276)(126,376)(127,380)(128,379)(129,378)(130,377)(131,400)(132,399)(133,398)(134,397)(135,396)(136,395)(137,394)(138,393)(139,392)(140,391)(141,390)(142,389)(143,388)(144,387)(145,386)(146,385)(147,384)(148,383)(149,382)(150,381)(151,500)(152,499)(153,498)(154,497)(155,496)(156,495)(157,494)(158,493)(159,492)(160,491)(161,490)(162,489)(163,488)(164,487)(165,486)(166,485)(167,484)(168,483)(169,482)(170,481)(171,480)(172,479)(173,478)(174,477)(175,476)(176,475)(177,474)(178,473)(179,472)(180,471)(181,470)(182,469)(183,468)(184,467)(185,466)(186,465)(187,464)(188,463)(189,462)(190,461)(191,460)(192,459)(193,458)(194,457)(195,456)(196,455)(197,454)(198,453)(199,452)(200,451)(201,450)(202,449)(203,448)(204,447)(205,446)(206,445)(207,444)(208,443)(209,442)(210,441)(211,440)(212,439)(213,438)(214,437)(215,436)(216,435)(217,434)(218,433)(219,432)(220,431)(221,430)(222,429)(223,428)(224,427)(225,426)(226,425)(227,424)(228,423)(229,422)(230,421)(231,420)(232,419)(233,418)(234,417)(235,416)(236,415)(237,414)(238,413)(239,412)(240,411)(241,410)(242,409)(243,408)(244,407)(245,406)(246,405)(247,404)(248,403)(249,402)(250,401);;
s2 := (  1, 26)(  2, 30)(  3, 29)(  4, 28)(  5, 27)(  6, 50)(  7, 49)(  8, 48)(  9, 47)( 10, 46)( 11, 45)( 12, 44)( 13, 43)( 14, 42)( 15, 41)( 16, 40)( 17, 39)( 18, 38)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)( 24, 32)( 25, 31)( 51,125)( 52,124)( 53,123)( 54,122)( 55,121)( 56,120)( 57,119)( 58,118)( 59,117)( 60,116)( 61,115)( 62,114)( 63,113)( 64,112)( 65,111)( 66,110)( 67,109)( 68,108)( 69,107)( 70,106)( 71,105)( 72,104)( 73,103)( 74,102)( 75,101)( 76,100)( 77, 99)( 78, 98)( 79, 97)( 80, 96)( 81, 95)( 82, 94)( 83, 93)( 84, 92)( 85, 91)( 86, 90)( 87, 89)(126,151)(127,155)(128,154)(129,153)(130,152)(131,175)(132,174)(133,173)(134,172)(135,171)(136,170)(137,169)(138,168)(139,167)(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(176,250)(177,249)(178,248)(179,247)(180,246)(181,245)(182,244)(183,243)(184,242)(185,241)(186,240)(187,239)(188,238)(189,237)(190,236)(191,235)(192,234)(193,233)(194,232)(195,231)(196,230)(197,229)(198,228)(199,227)(200,226)(201,225)(202,224)(203,223)(204,222)(205,221)(206,220)(207,219)(208,218)(209,217)(210,216)(211,215)(212,214)(251,276)(252,280)(253,279)(254,278)(255,277)(256,300)(257,299)(258,298)(259,297)(260,296)(261,295)(262,294)(263,293)(264,292)(265,291)(266,290)(267,289)(268,288)(269,287)(270,286)(271,285)(272,284)(273,283)(274,282)(275,281)(301,375)(302,374)(303,373)(304,372)(305,371)(306,370)(307,369)(308,368)(309,367)(310,366)(311,365)(312,364)(313,363)(314,362)(315,361)(316,360)(317,359)(318,358)(319,357)(320,356)(321,355)(322,354)(323,353)(324,352)(325,351)(326,350)(327,349)(328,348)(329,347)(330,346)(331,345)(332,344)(333,343)(334,342)(335,341)(336,340)(337,339)(376,401)(377,405)(378,404)(379,403)(380,402)(381,425)(382,424)(383,423)(384,422)(385,421)(386,420)(387,419)(388,418)(389,417)(390,416)(391,415)(392,414)(393,413)(394,412)(395,411)(396,410)(397,409)(398,408)(399,407)(400,406)(426,500)(427,499)(428,498)(429,497)(430,496)(431,495)(432,494)(433,493)(434,492)(435,491)(436,490)(437,489)(438,488)(439,487)(440,486)(441,485)(442,484)(443,483)(444,482)(445,481)(446,480)(447,479)(448,478)(449,477)(450,476)(451,475)(452,474)(453,473)(454,472)(455,471)(456,470)(457,469)(458,468)(459,467)(460,466)(461,465)(462,464);;
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*s0*s1*s0*s1*s0*s1, 
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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(500)!(251,376)(252,377)(253,378)(254,379)(255,380)(256,381)(257,382)(258,383)(259,384)(260,385)(261,386)(262,387)(263,388)(264,389)(265,390)(266,391)(267,392)(268,393)(269,394)(270,395)(271,396)(272,397)(273,398)(274,399)(275,400)(276,401)(277,402)(278,403)(279,404)(280,405)(281,406)(282,407)(283,408)(284,409)(285,410)(286,411)(287,412)(288,413)(289,414)(290,415)(291,416)(292,417)(293,418)(294,419)(295,420)(296,421)(297,422)(298,423)(299,424)(300,425)(301,426)(302,427)(303,428)(304,429)(305,430)(306,431)(307,432)(308,433)(309,434)(310,435)(311,436)(312,437)(313,438)(314,439)(315,440)(316,441)(317,442)(318,443)(319,444)(320,445)(321,446)(322,447)(323,448)(324,449)(325,450)(326,451)(327,452)(328,453)(329,454)(330,455)(331,456)(332,457)(333,458)(334,459)(335,460)(336,461)(337,462)(338,463)(339,464)(340,465)(341,466)(342,467)(343,468)(344,469)(345,470)(346,471)(347,472)(348,473)(349,474)(350,475)(351,476)(352,477)(353,478)(354,479)(355,480)(356,481)(357,482)(358,483)(359,484)(360,485)(361,486)(362,487)(363,488)(364,489)(365,490)(366,491)(367,492)(368,493)(369,494)(370,495)(371,496)(372,497)(373,498)(374,499)(375,500);
s1 := Sym(500)!(  1,251)(  2,255)(  3,254)(  4,253)(  5,252)(  6,275)(  7,274)(  8,273)(  9,272)( 10,271)( 11,270)( 12,269)( 13,268)( 14,267)( 15,266)( 16,265)( 17,264)( 18,263)( 19,262)( 20,261)( 21,260)( 22,259)( 23,258)( 24,257)( 25,256)( 26,375)( 27,374)( 28,373)( 29,372)( 30,371)( 31,370)( 32,369)( 33,368)( 34,367)( 35,366)( 36,365)( 37,364)( 38,363)( 39,362)( 40,361)( 41,360)( 42,359)( 43,358)( 44,357)( 45,356)( 46,355)( 47,354)( 48,353)( 49,352)( 50,351)( 51,350)( 52,349)( 53,348)( 54,347)( 55,346)( 56,345)( 57,344)( 58,343)( 59,342)( 60,341)( 61,340)( 62,339)( 63,338)( 64,337)( 65,336)( 66,335)( 67,334)( 68,333)( 69,332)( 70,331)( 71,330)( 72,329)( 73,328)( 74,327)( 75,326)( 76,325)( 77,324)( 78,323)( 79,322)( 80,321)( 81,320)( 82,319)( 83,318)( 84,317)( 85,316)( 86,315)( 87,314)( 88,313)( 89,312)( 90,311)( 91,310)( 92,309)( 93,308)( 94,307)( 95,306)( 96,305)( 97,304)( 98,303)( 99,302)(100,301)(101,300)(102,299)(103,298)(104,297)(105,296)(106,295)(107,294)(108,293)(109,292)(110,291)(111,290)(112,289)(113,288)(114,287)(115,286)(116,285)(117,284)(118,283)(119,282)(120,281)(121,280)(122,279)(123,278)(124,277)(125,276)(126,376)(127,380)(128,379)(129,378)(130,377)(131,400)(132,399)(133,398)(134,397)(135,396)(136,395)(137,394)(138,393)(139,392)(140,391)(141,390)(142,389)(143,388)(144,387)(145,386)(146,385)(147,384)(148,383)(149,382)(150,381)(151,500)(152,499)(153,498)(154,497)(155,496)(156,495)(157,494)(158,493)(159,492)(160,491)(161,490)(162,489)(163,488)(164,487)(165,486)(166,485)(167,484)(168,483)(169,482)(170,481)(171,480)(172,479)(173,478)(174,477)(175,476)(176,475)(177,474)(178,473)(179,472)(180,471)(181,470)(182,469)(183,468)(184,467)(185,466)(186,465)(187,464)(188,463)(189,462)(190,461)(191,460)(192,459)(193,458)(194,457)(195,456)(196,455)(197,454)(198,453)(199,452)(200,451)(201,450)(202,449)(203,448)(204,447)(205,446)(206,445)(207,444)(208,443)(209,442)(210,441)(211,440)(212,439)(213,438)(214,437)(215,436)(216,435)(217,434)(218,433)(219,432)(220,431)(221,430)(222,429)(223,428)(224,427)(225,426)(226,425)(227,424)(228,423)(229,422)(230,421)(231,420)(232,419)(233,418)(234,417)(235,416)(236,415)(237,414)(238,413)(239,412)(240,411)(241,410)(242,409)(243,408)(244,407)(245,406)(246,405)(247,404)(248,403)(249,402)(250,401);
s2 := Sym(500)!(  1, 26)(  2, 30)(  3, 29)(  4, 28)(  5, 27)(  6, 50)(  7, 49)(  8, 48)(  9, 47)( 10, 46)( 11, 45)( 12, 44)( 13, 43)( 14, 42)( 15, 41)( 16, 40)( 17, 39)( 18, 38)( 19, 37)( 20, 36)( 21, 35)( 22, 34)( 23, 33)( 24, 32)( 25, 31)( 51,125)( 52,124)( 53,123)( 54,122)( 55,121)( 56,120)( 57,119)( 58,118)( 59,117)( 60,116)( 61,115)( 62,114)( 63,113)( 64,112)( 65,111)( 66,110)( 67,109)( 68,108)( 69,107)( 70,106)( 71,105)( 72,104)( 73,103)( 74,102)( 75,101)( 76,100)( 77, 99)( 78, 98)( 79, 97)( 80, 96)( 81, 95)( 82, 94)( 83, 93)( 84, 92)( 85, 91)( 86, 90)( 87, 89)(126,151)(127,155)(128,154)(129,153)(130,152)(131,175)(132,174)(133,173)(134,172)(135,171)(136,170)(137,169)(138,168)(139,167)(140,166)(141,165)(142,164)(143,163)(144,162)(145,161)(146,160)(147,159)(148,158)(149,157)(150,156)(176,250)(177,249)(178,248)(179,247)(180,246)(181,245)(182,244)(183,243)(184,242)(185,241)(186,240)(187,239)(188,238)(189,237)(190,236)(191,235)(192,234)(193,233)(194,232)(195,231)(196,230)(197,229)(198,228)(199,227)(200,226)(201,225)(202,224)(203,223)(204,222)(205,221)(206,220)(207,219)(208,218)(209,217)(210,216)(211,215)(212,214)(251,276)(252,280)(253,279)(254,278)(255,277)(256,300)(257,299)(258,298)(259,297)(260,296)(261,295)(262,294)(263,293)(264,292)(265,291)(266,290)(267,289)(268,288)(269,287)(270,286)(271,285)(272,284)(273,283)(274,282)(275,281)(301,375)(302,374)(303,373)(304,372)(305,371)(306,370)(307,369)(308,368)(309,367)(310,366)(311,365)(312,364)(313,363)(314,362)(315,361)(316,360)(317,359)(318,358)(319,357)(320,356)(321,355)(322,354)(323,353)(324,352)(325,351)(326,350)(327,349)(328,348)(329,347)(330,346)(331,345)(332,344)(333,343)(334,342)(335,341)(336,340)(337,339)(376,401)(377,405)(378,404)(379,403)(380,402)(381,425)(382,424)(383,423)(384,422)(385,421)(386,420)(387,419)(388,418)(389,417)(390,416)(391,415)(392,414)(393,413)(394,412)(395,411)(396,410)(397,409)(398,408)(399,407)(400,406)(426,500)(427,499)(428,498)(429,497)(430,496)(431,495)(432,494)(433,493)(434,492)(435,491)(436,490)(437,489)(438,488)(439,487)(440,486)(441,485)(442,484)(443,483)(444,482)(445,481)(446,480)(447,479)(448,478)(449,477)(450,476)(451,475)(452,474)(453,473)(454,472)(455,471)(456,470)(457,469)(458,468)(459,467)(460,466)(461,465)(462,464);
poly := sub<Sym(500)|s0,s1,s2>;
 

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