Polytope of Type {8,68}

Play with this polytope as a twisty puzzle

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