Polytope of Type {68,8}

Play with this polytope as a twisty puzzle

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