Polytope of Type {20,50}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle