Polytope of Type {136,4}

Play with this polytope as a twisty puzzle

s0 := (  1,273)(  2,289)(  3,288)(  4,287)(  5,286)(  6,285)(  7,284)(  8,283)(  9,282)( 10,281)( 11,280)( 12,279)( 13,278)( 14,277)( 15,276)( 16,275)( 17,274)( 18,290)( 19,306)( 20,305)( 21,304)( 22,303)( 23,302)( 24,301)( 25,300)( 26,299)( 27,298)( 28,297)( 29,296)( 30,295)( 31,294)( 32,293)( 33,292)( 34,291)( 35,324)( 36,340)( 37,339)( 38,338)( 39,337)( 40,336)( 41,335)( 42,334)( 43,333)( 44,332)( 45,331)( 46,330)( 47,329)( 48,328)( 49,327)( 50,326)( 51,325)( 52,307)( 53,323)( 54,322)( 55,321)( 56,320)( 57,319)( 58,318)( 59,317)( 60,316)( 61,315)( 62,314)( 63,313)( 64,312)( 65,311)( 66,310)( 67,309)( 68,308)( 69,358)( 70,374)( 71,373)( 72,372)( 73,371)( 74,370)( 75,369)( 76,368)( 77,367)( 78,366)( 79,365)( 80,364)( 81,363)( 82,362)( 83,361)( 84,360)( 85,359)( 86,341)( 87,357)( 88,356)( 89,355)( 90,354)( 91,353)( 92,352)( 93,351)( 94,350)( 95,349)( 96,348)( 97,347)( 98,346)( 99,345)(100,344)(101,343)(102,342)(103,375)(104,391)(105,390)(106,389)(107,388)(108,387)(109,386)(110,385)(111,384)(112,383)(113,382)(114,381)(115,380)(116,379)(117,378)(118,377)(119,376)(120,392)(121,408)(122,407)(123,406)(124,405)(125,404)(126,403)(127,402)(128,401)(129,400)(130,399)(131,398)(132,397)(133,396)(134,395)(135,394)(136,393)(137,409)(138,425)(139,424)(140,423)(141,422)(142,421)(143,420)(144,419)(145,418)(146,417)(147,416)(148,415)(149,414)(150,413)(151,412)(152,411)(153,410)(154,426)(155,442)(156,441)(157,440)(158,439)(159,438)(160,437)(161,436)(162,435)(163,434)(164,433)(165,432)(166,431)(167,430)(168,429)(169,428)(170,427)(171,460)(172,476)(173,475)(174,474)(175,473)(176,472)(177,471)(178,470)(179,469)(180,468)(181,467)(182,466)(183,465)(184,464)(185,463)(186,462)(187,461)(188,443)(189,459)(190,458)(191,457)(192,456)(193,455)(194,454)(195,453)(196,452)(197,451)(198,450)(199,449)(200,448)(201,447)(202,446)(203,445)(204,444)(205,494)(206,510)(207,509)(208,508)(209,507)(210,506)(211,505)(212,504)(213,503)(214,502)(215,501)(216,500)(217,499)(218,498)(219,497)(220,496)(221,495)(222,477)(223,493)(224,492)(225,491)(226,490)(227,489)(228,488)(229,487)(230,486)(231,485)(232,484)(233,483)(234,482)(235,481)(236,480)(237,479)(238,478)(239,511)(240,527)(241,526)(242,525)(243,524)(244,523)(245,522)(246,521)(247,520)(248,519)(249,518)(250,517)(251,516)(252,515)(253,514)(254,513)(255,512)(256,528)(257,544)(258,543)(259,542)(260,541)(261,540)(262,539)(263,538)(264,537)(265,536)(266,535)(267,534)(268,533)(269,532)(270,531)(271,530)(272,529);;
s1 := (  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)( 75, 98)( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)(103,121)(104,120)(105,136)(106,135)(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(137,172)(138,171)(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,173)(154,189)(155,188)(156,204)(157,203)(158,202)(159,201)(160,200)(161,199)(162,198)(163,197)(164,196)(165,195)(166,194)(167,193)(168,192)(169,191)(170,190)(205,257)(206,256)(207,272)(208,271)(209,270)(210,269)(211,268)(212,267)(213,266)(214,265)(215,264)(216,263)(217,262)(218,261)(219,260)(220,259)(221,258)(222,240)(223,239)(224,255)(225,254)(226,253)(227,252)(228,251)(229,250)(230,249)(231,248)(232,247)(233,246)(234,245)(235,244)(236,243)(237,242)(238,241)(273,342)(274,341)(275,357)(276,356)(277,355)(278,354)(279,353)(280,352)(281,351)(282,350)(283,349)(284,348)(285,347)(286,346)(287,345)(288,344)(289,343)(290,359)(291,358)(292,374)(293,373)(294,372)(295,371)(296,370)(297,369)(298,368)(299,367)(300,366)(301,365)(302,364)(303,363)(304,362)(305,361)(306,360)(307,376)(308,375)(309,391)(310,390)(311,389)(312,388)(313,387)(314,386)(315,385)(316,384)(317,383)(318,382)(319,381)(320,380)(321,379)(322,378)(323,377)(324,393)(325,392)(326,408)(327,407)(328,406)(329,405)(330,404)(331,403)(332,402)(333,401)(334,400)(335,399)(336,398)(337,397)(338,396)(339,395)(340,394)(409,529)(410,528)(411,544)(412,543)(413,542)(414,541)(415,540)(416,539)(417,538)(418,537)(419,536)(420,535)(421,534)(422,533)(423,532)(424,531)(425,530)(426,512)(427,511)(428,527)(429,526)(430,525)(431,524)(432,523)(433,522)(434,521)(435,520)(436,519)(437,518)(438,517)(439,516)(440,515)(441,514)(442,513)(443,495)(444,494)(445,510)(446,509)(447,508)(448,507)(449,506)(450,505)(451,504)(452,503)(453,502)(454,501)(455,500)(456,499)(457,498)(458,497)(459,496)(460,478)(461,477)(462,493)(463,492)(464,491)(465,490)(466,489)(467,488)(468,487)(469,486)(470,485)(471,484)(472,483)(473,482)(474,481)(475,480)(476,479);;
s2 := (  1,137)(  2,138)(  3,139)(  4,140)(  5,141)(  6,142)(  7,143)(  8,144)(  9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)( 16,152)( 17,153)( 18,154)( 19,155)( 20,156)( 21,157)( 22,158)( 23,159)( 24,160)( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)( 32,168)( 33,169)( 34,170)( 35,171)( 36,172)( 37,173)( 38,174)( 39,175)( 40,176)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)( 49,185)( 50,186)( 51,187)( 52,188)( 53,189)( 54,190)( 55,191)( 56,192)( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)( 64,200)( 65,201)( 66,202)( 67,203)( 68,204)( 69,222)( 70,223)( 71,224)( 72,225)( 73,226)( 74,227)( 75,228)( 76,229)( 77,230)( 78,231)( 79,232)( 80,233)( 81,234)( 82,235)( 83,236)( 84,237)( 85,238)( 86,205)( 87,206)( 88,207)( 89,208)( 90,209)( 91,210)( 92,211)( 93,212)( 94,213)( 95,214)( 96,215)( 97,216)( 98,217)( 99,218)(100,219)(101,220)(102,221)(103,256)(104,257)(105,258)(106,259)(107,260)(108,261)(109,262)(110,263)(111,264)(112,265)(113,266)(114,267)(115,268)(116,269)(117,270)(118,271)(119,272)(120,239)(121,240)(122,241)(123,242)(124,243)(125,244)(126,245)(127,246)(128,247)(129,248)(130,249)(131,250)(132,251)(133,252)(134,253)(135,254)(136,255)(273,409)(274,410)(275,411)(276,412)(277,413)(278,414)(279,415)(280,416)(281,417)(282,418)(283,419)(284,420)(285,421)(286,422)(287,423)(288,424)(289,425)(290,426)(291,427)(292,428)(293,429)(294,430)(295,431)(296,432)(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)(304,440)(305,441)(306,442)(307,443)(308,444)(309,445)(310,446)(311,447)(312,448)(313,449)(314,450)(315,451)(316,452)(317,453)(318,454)(319,455)(320,456)(321,457)(322,458)(323,459)(324,460)(325,461)(326,462)(327,463)(328,464)(329,465)(330,466)(331,467)(332,468)(333,469)(334,470)(335,471)(336,472)(337,473)(338,474)(339,475)(340,476)(341,494)(342,495)(343,496)(344,497)(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)(352,505)(353,506)(354,507)(355,508)(356,509)(357,510)(358,477)(359,478)(360,479)(361,480)(362,481)(363,482)(364,483)(365,484)(366,485)(367,486)(368,487)(369,488)(370,489)(371,490)(372,491)(373,492)(374,493)(375,528)(376,529)(377,530)(378,531)(379,532)(380,533)(381,534)(382,535)(383,536)(384,537)(385,538)(386,539)(387,540)(388,541)(389,542)(390,543)(391,544)(392,511)(393,512)(394,513)(395,514)(396,515)(397,516)(398,517)(399,518)(400,519)(401,520)(402,521)(403,522)(404,523)(405,524)(406,525)(407,526)(408,527);;
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, s1*s2*s1*s2*s1*s2*s1*s2, 
s0*s2*s1*s2*s1*s0*s1*s0*s2*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*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*s2*s1*s0*s1*s0*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*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(544)!(  1,273)(  2,289)(  3,288)(  4,287)(  5,286)(  6,285)(  7,284)(  8,283)(  9,282)( 10,281)( 11,280)( 12,279)( 13,278)( 14,277)( 15,276)( 16,275)( 17,274)( 18,290)( 19,306)( 20,305)( 21,304)( 22,303)( 23,302)( 24,301)( 25,300)( 26,299)( 27,298)( 28,297)( 29,296)( 30,295)( 31,294)( 32,293)( 33,292)( 34,291)( 35,324)( 36,340)( 37,339)( 38,338)( 39,337)( 40,336)( 41,335)( 42,334)( 43,333)( 44,332)( 45,331)( 46,330)( 47,329)( 48,328)( 49,327)( 50,326)( 51,325)( 52,307)( 53,323)( 54,322)( 55,321)( 56,320)( 57,319)( 58,318)( 59,317)( 60,316)( 61,315)( 62,314)( 63,313)( 64,312)( 65,311)( 66,310)( 67,309)( 68,308)( 69,358)( 70,374)( 71,373)( 72,372)( 73,371)( 74,370)( 75,369)( 76,368)( 77,367)( 78,366)( 79,365)( 80,364)( 81,363)( 82,362)( 83,361)( 84,360)( 85,359)( 86,341)( 87,357)( 88,356)( 89,355)( 90,354)( 91,353)( 92,352)( 93,351)( 94,350)( 95,349)( 96,348)( 97,347)( 98,346)( 99,345)(100,344)(101,343)(102,342)(103,375)(104,391)(105,390)(106,389)(107,388)(108,387)(109,386)(110,385)(111,384)(112,383)(113,382)(114,381)(115,380)(116,379)(117,378)(118,377)(119,376)(120,392)(121,408)(122,407)(123,406)(124,405)(125,404)(126,403)(127,402)(128,401)(129,400)(130,399)(131,398)(132,397)(133,396)(134,395)(135,394)(136,393)(137,409)(138,425)(139,424)(140,423)(141,422)(142,421)(143,420)(144,419)(145,418)(146,417)(147,416)(148,415)(149,414)(150,413)(151,412)(152,411)(153,410)(154,426)(155,442)(156,441)(157,440)(158,439)(159,438)(160,437)(161,436)(162,435)(163,434)(164,433)(165,432)(166,431)(167,430)(168,429)(169,428)(170,427)(171,460)(172,476)(173,475)(174,474)(175,473)(176,472)(177,471)(178,470)(179,469)(180,468)(181,467)(182,466)(183,465)(184,464)(185,463)(186,462)(187,461)(188,443)(189,459)(190,458)(191,457)(192,456)(193,455)(194,454)(195,453)(196,452)(197,451)(198,450)(199,449)(200,448)(201,447)(202,446)(203,445)(204,444)(205,494)(206,510)(207,509)(208,508)(209,507)(210,506)(211,505)(212,504)(213,503)(214,502)(215,501)(216,500)(217,499)(218,498)(219,497)(220,496)(221,495)(222,477)(223,493)(224,492)(225,491)(226,490)(227,489)(228,488)(229,487)(230,486)(231,485)(232,484)(233,483)(234,482)(235,481)(236,480)(237,479)(238,478)(239,511)(240,527)(241,526)(242,525)(243,524)(244,523)(245,522)(246,521)(247,520)(248,519)(249,518)(250,517)(251,516)(252,515)(253,514)(254,513)(255,512)(256,528)(257,544)(258,543)(259,542)(260,541)(261,540)(262,539)(263,538)(264,537)(265,536)(266,535)(267,534)(268,533)(269,532)(270,531)(271,530)(272,529);
s1 := Sym(544)!(  1,  2)(  3, 17)(  4, 16)(  5, 15)(  6, 14)(  7, 13)(  8, 12)(  9, 11)( 18, 19)( 20, 34)( 21, 33)( 22, 32)( 23, 31)( 24, 30)( 25, 29)( 26, 28)( 35, 36)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)( 52, 53)( 54, 68)( 55, 67)( 56, 66)( 57, 65)( 58, 64)( 59, 63)( 60, 62)( 69, 87)( 70, 86)( 71,102)( 72,101)( 73,100)( 74, 99)( 75, 98)( 76, 97)( 77, 96)( 78, 95)( 79, 94)( 80, 93)( 81, 92)( 82, 91)( 83, 90)( 84, 89)( 85, 88)(103,121)(104,120)(105,136)(106,135)(107,134)(108,133)(109,132)(110,131)(111,130)(112,129)(113,128)(114,127)(115,126)(116,125)(117,124)(118,123)(119,122)(137,172)(138,171)(139,187)(140,186)(141,185)(142,184)(143,183)(144,182)(145,181)(146,180)(147,179)(148,178)(149,177)(150,176)(151,175)(152,174)(153,173)(154,189)(155,188)(156,204)(157,203)(158,202)(159,201)(160,200)(161,199)(162,198)(163,197)(164,196)(165,195)(166,194)(167,193)(168,192)(169,191)(170,190)(205,257)(206,256)(207,272)(208,271)(209,270)(210,269)(211,268)(212,267)(213,266)(214,265)(215,264)(216,263)(217,262)(218,261)(219,260)(220,259)(221,258)(222,240)(223,239)(224,255)(225,254)(226,253)(227,252)(228,251)(229,250)(230,249)(231,248)(232,247)(233,246)(234,245)(235,244)(236,243)(237,242)(238,241)(273,342)(274,341)(275,357)(276,356)(277,355)(278,354)(279,353)(280,352)(281,351)(282,350)(283,349)(284,348)(285,347)(286,346)(287,345)(288,344)(289,343)(290,359)(291,358)(292,374)(293,373)(294,372)(295,371)(296,370)(297,369)(298,368)(299,367)(300,366)(301,365)(302,364)(303,363)(304,362)(305,361)(306,360)(307,376)(308,375)(309,391)(310,390)(311,389)(312,388)(313,387)(314,386)(315,385)(316,384)(317,383)(318,382)(319,381)(320,380)(321,379)(322,378)(323,377)(324,393)(325,392)(326,408)(327,407)(328,406)(329,405)(330,404)(331,403)(332,402)(333,401)(334,400)(335,399)(336,398)(337,397)(338,396)(339,395)(340,394)(409,529)(410,528)(411,544)(412,543)(413,542)(414,541)(415,540)(416,539)(417,538)(418,537)(419,536)(420,535)(421,534)(422,533)(423,532)(424,531)(425,530)(426,512)(427,511)(428,527)(429,526)(430,525)(431,524)(432,523)(433,522)(434,521)(435,520)(436,519)(437,518)(438,517)(439,516)(440,515)(441,514)(442,513)(443,495)(444,494)(445,510)(446,509)(447,508)(448,507)(449,506)(450,505)(451,504)(452,503)(453,502)(454,501)(455,500)(456,499)(457,498)(458,497)(459,496)(460,478)(461,477)(462,493)(463,492)(464,491)(465,490)(466,489)(467,488)(468,487)(469,486)(470,485)(471,484)(472,483)(473,482)(474,481)(475,480)(476,479);
s2 := Sym(544)!(  1,137)(  2,138)(  3,139)(  4,140)(  5,141)(  6,142)(  7,143)(  8,144)(  9,145)( 10,146)( 11,147)( 12,148)( 13,149)( 14,150)( 15,151)( 16,152)( 17,153)( 18,154)( 19,155)( 20,156)( 21,157)( 22,158)( 23,159)( 24,160)( 25,161)( 26,162)( 27,163)( 28,164)( 29,165)( 30,166)( 31,167)( 32,168)( 33,169)( 34,170)( 35,171)( 36,172)( 37,173)( 38,174)( 39,175)( 40,176)( 41,177)( 42,178)( 43,179)( 44,180)( 45,181)( 46,182)( 47,183)( 48,184)( 49,185)( 50,186)( 51,187)( 52,188)( 53,189)( 54,190)( 55,191)( 56,192)( 57,193)( 58,194)( 59,195)( 60,196)( 61,197)( 62,198)( 63,199)( 64,200)( 65,201)( 66,202)( 67,203)( 68,204)( 69,222)( 70,223)( 71,224)( 72,225)( 73,226)( 74,227)( 75,228)( 76,229)( 77,230)( 78,231)( 79,232)( 80,233)( 81,234)( 82,235)( 83,236)( 84,237)( 85,238)( 86,205)( 87,206)( 88,207)( 89,208)( 90,209)( 91,210)( 92,211)( 93,212)( 94,213)( 95,214)( 96,215)( 97,216)( 98,217)( 99,218)(100,219)(101,220)(102,221)(103,256)(104,257)(105,258)(106,259)(107,260)(108,261)(109,262)(110,263)(111,264)(112,265)(113,266)(114,267)(115,268)(116,269)(117,270)(118,271)(119,272)(120,239)(121,240)(122,241)(123,242)(124,243)(125,244)(126,245)(127,246)(128,247)(129,248)(130,249)(131,250)(132,251)(133,252)(134,253)(135,254)(136,255)(273,409)(274,410)(275,411)(276,412)(277,413)(278,414)(279,415)(280,416)(281,417)(282,418)(283,419)(284,420)(285,421)(286,422)(287,423)(288,424)(289,425)(290,426)(291,427)(292,428)(293,429)(294,430)(295,431)(296,432)(297,433)(298,434)(299,435)(300,436)(301,437)(302,438)(303,439)(304,440)(305,441)(306,442)(307,443)(308,444)(309,445)(310,446)(311,447)(312,448)(313,449)(314,450)(315,451)(316,452)(317,453)(318,454)(319,455)(320,456)(321,457)(322,458)(323,459)(324,460)(325,461)(326,462)(327,463)(328,464)(329,465)(330,466)(331,467)(332,468)(333,469)(334,470)(335,471)(336,472)(337,473)(338,474)(339,475)(340,476)(341,494)(342,495)(343,496)(344,497)(345,498)(346,499)(347,500)(348,501)(349,502)(350,503)(351,504)(352,505)(353,506)(354,507)(355,508)(356,509)(357,510)(358,477)(359,478)(360,479)(361,480)(362,481)(363,482)(364,483)(365,484)(366,485)(367,486)(368,487)(369,488)(370,489)(371,490)(372,491)(373,492)(374,493)(375,528)(376,529)(377,530)(378,531)(379,532)(380,533)(381,534)(382,535)(383,536)(384,537)(385,538)(386,539)(387,540)(388,541)(389,542)(390,543)(391,544)(392,511)(393,512)(394,513)(395,514)(396,515)(397,516)(398,517)(399,518)(400,519)(401,520)(402,521)(403,522)(404,523)(405,524)(406,525)(407,526)(408,527);
poly := sub<Sym(544)|s0,s1,s2>;
 

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

Twisty Puzzle