Polytope of Type {8,74}

Play with this polytope as a twisty puzzle

s0 := ( 75,112)( 76,113)( 77,114)( 78,115)( 79,116)( 80,117)( 81,118)( 82,119)( 83,120)( 84,121)( 85,122)( 86,123)( 87,124)( 88,125)( 89,126)( 90,127)( 91,128)( 92,129)( 93,130)( 94,131)( 95,132)( 96,133)( 97,134)( 98,135)( 99,136)(100,137)(101,138)(102,139)(103,140)(104,141)(105,142)(106,143)(107,144)(108,145)(109,146)(110,147)(111,148)(223,260)(224,261)(225,262)(226,263)(227,264)(228,265)(229,266)(230,267)(231,268)(232,269)(233,270)(234,271)(235,272)(236,273)(237,274)(238,275)(239,276)(240,277)(241,278)(242,279)(243,280)(244,281)(245,282)(246,283)(247,284)(248,285)(249,286)(250,287)(251,288)(252,289)(253,290)(254,291)(255,292)(256,293)(257,294)(258,295)(259,296)(297,371)(298,372)(299,373)(300,374)(301,375)(302,376)(303,377)(304,378)(305,379)(306,380)(307,381)(308,382)(309,383)(310,384)(311,385)(312,386)(313,387)(314,388)(315,389)(316,390)(317,391)(318,392)(319,393)(320,394)(321,395)(322,396)(323,397)(324,398)(325,399)(326,400)(327,401)(328,402)(329,403)(330,404)(331,405)(332,406)(333,407)(334,408)(335,409)(336,410)(337,411)(338,412)(339,413)(340,414)(341,415)(342,416)(343,417)(344,418)(345,419)(346,420)(347,421)(348,422)(349,423)(350,424)(351,425)(352,426)(353,427)(354,428)(355,429)(356,430)(357,431)(358,432)(359,433)(360,434)(361,435)(362,436)(363,437)(364,438)(365,439)(366,440)(367,441)(368,442)(369,443)(370,444)(445,519)(446,520)(447,521)(448,522)(449,523)(450,524)(451,525)(452,526)(453,527)(454,528)(455,529)(456,530)(457,531)(458,532)(459,533)(460,534)(461,535)(462,536)(463,537)(464,538)(465,539)(466,540)(467,541)(468,542)(469,543)(470,544)(471,545)(472,546)(473,547)(474,548)(475,549)(476,550)(477,551)(478,552)(479,553)(480,554)(481,555)(482,556)(483,557)(484,558)(485,559)(486,560)(487,561)(488,562)(489,563)(490,564)(491,565)(492,566)(493,567)(494,568)(495,569)(496,570)(497,571)(498,572)(499,573)(500,574)(501,575)(502,576)(503,577)(504,578)(505,579)(506,580)(507,581)(508,582)(509,583)(510,584)(511,585)(512,586)(513,587)(514,588)(515,589)(516,590)(517,591)(518,592);;
s1 := (  1,445)(  2,481)(  3,480)(  4,479)(  5,478)(  6,477)(  7,476)(  8,475)(  9,474)( 10,473)( 11,472)( 12,471)( 13,470)( 14,469)( 15,468)( 16,467)( 17,466)( 18,465)( 19,464)( 20,463)( 21,462)( 22,461)( 23,460)( 24,459)( 25,458)( 26,457)( 27,456)( 28,455)( 29,454)( 30,453)( 31,452)( 32,451)( 33,450)( 34,449)( 35,448)( 36,447)( 37,446)( 38,482)( 39,518)( 40,517)( 41,516)( 42,515)( 43,514)( 44,513)( 45,512)( 46,511)( 47,510)( 48,509)( 49,508)( 50,507)( 51,506)( 52,505)( 53,504)( 54,503)( 55,502)( 56,501)( 57,500)( 58,499)( 59,498)( 60,497)( 61,496)( 62,495)( 63,494)( 64,493)( 65,492)( 66,491)( 67,490)( 68,489)( 69,488)( 70,487)( 71,486)( 72,485)( 73,484)( 74,483)( 75,556)( 76,592)( 77,591)( 78,590)( 79,589)( 80,588)( 81,587)( 82,586)( 83,585)( 84,584)( 85,583)( 86,582)( 87,581)( 88,580)( 89,579)( 90,578)( 91,577)( 92,576)( 93,575)( 94,574)( 95,573)( 96,572)( 97,571)( 98,570)( 99,569)(100,568)(101,567)(102,566)(103,565)(104,564)(105,563)(106,562)(107,561)(108,560)(109,559)(110,558)(111,557)(112,519)(113,555)(114,554)(115,553)(116,552)(117,551)(118,550)(119,549)(120,548)(121,547)(122,546)(123,545)(124,544)(125,543)(126,542)(127,541)(128,540)(129,539)(130,538)(131,537)(132,536)(133,535)(134,534)(135,533)(136,532)(137,531)(138,530)(139,529)(140,528)(141,527)(142,526)(143,525)(144,524)(145,523)(146,522)(147,521)(148,520)(149,297)(150,333)(151,332)(152,331)(153,330)(154,329)(155,328)(156,327)(157,326)(158,325)(159,324)(160,323)(161,322)(162,321)(163,320)(164,319)(165,318)(166,317)(167,316)(168,315)(169,314)(170,313)(171,312)(172,311)(173,310)(174,309)(175,308)(176,307)(177,306)(178,305)(179,304)(180,303)(181,302)(182,301)(183,300)(184,299)(185,298)(186,334)(187,370)(188,369)(189,368)(190,367)(191,366)(192,365)(193,364)(194,363)(195,362)(196,361)(197,360)(198,359)(199,358)(200,357)(201,356)(202,355)(203,354)(204,353)(205,352)(206,351)(207,350)(208,349)(209,348)(210,347)(211,346)(212,345)(213,344)(214,343)(215,342)(216,341)(217,340)(218,339)(219,338)(220,337)(221,336)(222,335)(223,408)(224,444)(225,443)(226,442)(227,441)(228,440)(229,439)(230,438)(231,437)(232,436)(233,435)(234,434)(235,433)(236,432)(237,431)(238,430)(239,429)(240,428)(241,427)(242,426)(243,425)(244,424)(245,423)(246,422)(247,421)(248,420)(249,419)(250,418)(251,417)(252,416)(253,415)(254,414)(255,413)(256,412)(257,411)(258,410)(259,409)(260,371)(261,407)(262,406)(263,405)(264,404)(265,403)(266,402)(267,401)(268,400)(269,399)(270,398)(271,397)(272,396)(273,395)(274,394)(275,393)(276,392)(277,391)(278,390)(279,389)(280,388)(281,387)(282,386)(283,385)(284,384)(285,383)(286,382)(287,381)(288,380)(289,379)(290,378)(291,377)(292,376)(293,375)(294,374)(295,373)(296,372);;
s2 := (  1,150)(  2,149)(  3,185)(  4,184)(  5,183)(  6,182)(  7,181)(  8,180)(  9,179)( 10,178)( 11,177)( 12,176)( 13,175)( 14,174)( 15,173)( 16,172)( 17,171)( 18,170)( 19,169)( 20,168)( 21,167)( 22,166)( 23,165)( 24,164)( 25,163)( 26,162)( 27,161)( 28,160)( 29,159)( 30,158)( 31,157)( 32,156)( 33,155)( 34,154)( 35,153)( 36,152)( 37,151)( 38,187)( 39,186)( 40,222)( 41,221)( 42,220)( 43,219)( 44,218)( 45,217)( 46,216)( 47,215)( 48,214)( 49,213)( 50,212)( 51,211)( 52,210)( 53,209)( 54,208)( 55,207)( 56,206)( 57,205)( 58,204)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)( 64,198)( 65,197)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,191)( 72,190)( 73,189)( 74,188)( 75,224)( 76,223)( 77,259)( 78,258)( 79,257)( 80,256)( 81,255)( 82,254)( 83,253)( 84,252)( 85,251)( 86,250)( 87,249)( 88,248)( 89,247)( 90,246)( 91,245)( 92,244)( 93,243)( 94,242)( 95,241)( 96,240)( 97,239)( 98,238)( 99,237)(100,236)(101,235)(102,234)(103,233)(104,232)(105,231)(106,230)(107,229)(108,228)(109,227)(110,226)(111,225)(112,261)(113,260)(114,296)(115,295)(116,294)(117,293)(118,292)(119,291)(120,290)(121,289)(122,288)(123,287)(124,286)(125,285)(126,284)(127,283)(128,282)(129,281)(130,280)(131,279)(132,278)(133,277)(134,276)(135,275)(136,274)(137,273)(138,272)(139,271)(140,270)(141,269)(142,268)(143,267)(144,266)(145,265)(146,264)(147,263)(148,262)(297,446)(298,445)(299,481)(300,480)(301,479)(302,478)(303,477)(304,476)(305,475)(306,474)(307,473)(308,472)(309,471)(310,470)(311,469)(312,468)(313,467)(314,466)(315,465)(316,464)(317,463)(318,462)(319,461)(320,460)(321,459)(322,458)(323,457)(324,456)(325,455)(326,454)(327,453)(328,452)(329,451)(330,450)(331,449)(332,448)(333,447)(334,483)(335,482)(336,518)(337,517)(338,516)(339,515)(340,514)(341,513)(342,512)(343,511)(344,510)(345,509)(346,508)(347,507)(348,506)(349,505)(350,504)(351,503)(352,502)(353,501)(354,500)(355,499)(356,498)(357,497)(358,496)(359,495)(360,494)(361,493)(362,492)(363,491)(364,490)(365,489)(366,488)(367,487)(368,486)(369,485)(370,484)(371,520)(372,519)(373,555)(374,554)(375,553)(376,552)(377,551)(378,550)(379,549)(380,548)(381,547)(382,546)(383,545)(384,544)(385,543)(386,542)(387,541)(388,540)(389,539)(390,538)(391,537)(392,536)(393,535)(394,534)(395,533)(396,532)(397,531)(398,530)(399,529)(400,528)(401,527)(402,526)(403,525)(404,524)(405,523)(406,522)(407,521)(408,557)(409,556)(410,592)(411,591)(412,590)(413,589)(414,588)(415,587)(416,586)(417,585)(418,584)(419,583)(420,582)(421,581)(422,580)(423,579)(424,578)(425,577)(426,576)(427,575)(428,574)(429,573)(430,572)(431,571)(432,570)(433,569)(434,568)(435,567)(436,566)(437,565)(438,564)(439,563)(440,562)(441,561)(442,560)(443,559)(444,558);;
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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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(592)!( 75,112)( 76,113)( 77,114)( 78,115)( 79,116)( 80,117)( 81,118)( 82,119)( 83,120)( 84,121)( 85,122)( 86,123)( 87,124)( 88,125)( 89,126)( 90,127)( 91,128)( 92,129)( 93,130)( 94,131)( 95,132)( 96,133)( 97,134)( 98,135)( 99,136)(100,137)(101,138)(102,139)(103,140)(104,141)(105,142)(106,143)(107,144)(108,145)(109,146)(110,147)(111,148)(223,260)(224,261)(225,262)(226,263)(227,264)(228,265)(229,266)(230,267)(231,268)(232,269)(233,270)(234,271)(235,272)(236,273)(237,274)(238,275)(239,276)(240,277)(241,278)(242,279)(243,280)(244,281)(245,282)(246,283)(247,284)(248,285)(249,286)(250,287)(251,288)(252,289)(253,290)(254,291)(255,292)(256,293)(257,294)(258,295)(259,296)(297,371)(298,372)(299,373)(300,374)(301,375)(302,376)(303,377)(304,378)(305,379)(306,380)(307,381)(308,382)(309,383)(310,384)(311,385)(312,386)(313,387)(314,388)(315,389)(316,390)(317,391)(318,392)(319,393)(320,394)(321,395)(322,396)(323,397)(324,398)(325,399)(326,400)(327,401)(328,402)(329,403)(330,404)(331,405)(332,406)(333,407)(334,408)(335,409)(336,410)(337,411)(338,412)(339,413)(340,414)(341,415)(342,416)(343,417)(344,418)(345,419)(346,420)(347,421)(348,422)(349,423)(350,424)(351,425)(352,426)(353,427)(354,428)(355,429)(356,430)(357,431)(358,432)(359,433)(360,434)(361,435)(362,436)(363,437)(364,438)(365,439)(366,440)(367,441)(368,442)(369,443)(370,444)(445,519)(446,520)(447,521)(448,522)(449,523)(450,524)(451,525)(452,526)(453,527)(454,528)(455,529)(456,530)(457,531)(458,532)(459,533)(460,534)(461,535)(462,536)(463,537)(464,538)(465,539)(466,540)(467,541)(468,542)(469,543)(470,544)(471,545)(472,546)(473,547)(474,548)(475,549)(476,550)(477,551)(478,552)(479,553)(480,554)(481,555)(482,556)(483,557)(484,558)(485,559)(486,560)(487,561)(488,562)(489,563)(490,564)(491,565)(492,566)(493,567)(494,568)(495,569)(496,570)(497,571)(498,572)(499,573)(500,574)(501,575)(502,576)(503,577)(504,578)(505,579)(506,580)(507,581)(508,582)(509,583)(510,584)(511,585)(512,586)(513,587)(514,588)(515,589)(516,590)(517,591)(518,592);
s1 := Sym(592)!(  1,445)(  2,481)(  3,480)(  4,479)(  5,478)(  6,477)(  7,476)(  8,475)(  9,474)( 10,473)( 11,472)( 12,471)( 13,470)( 14,469)( 15,468)( 16,467)( 17,466)( 18,465)( 19,464)( 20,463)( 21,462)( 22,461)( 23,460)( 24,459)( 25,458)( 26,457)( 27,456)( 28,455)( 29,454)( 30,453)( 31,452)( 32,451)( 33,450)( 34,449)( 35,448)( 36,447)( 37,446)( 38,482)( 39,518)( 40,517)( 41,516)( 42,515)( 43,514)( 44,513)( 45,512)( 46,511)( 47,510)( 48,509)( 49,508)( 50,507)( 51,506)( 52,505)( 53,504)( 54,503)( 55,502)( 56,501)( 57,500)( 58,499)( 59,498)( 60,497)( 61,496)( 62,495)( 63,494)( 64,493)( 65,492)( 66,491)( 67,490)( 68,489)( 69,488)( 70,487)( 71,486)( 72,485)( 73,484)( 74,483)( 75,556)( 76,592)( 77,591)( 78,590)( 79,589)( 80,588)( 81,587)( 82,586)( 83,585)( 84,584)( 85,583)( 86,582)( 87,581)( 88,580)( 89,579)( 90,578)( 91,577)( 92,576)( 93,575)( 94,574)( 95,573)( 96,572)( 97,571)( 98,570)( 99,569)(100,568)(101,567)(102,566)(103,565)(104,564)(105,563)(106,562)(107,561)(108,560)(109,559)(110,558)(111,557)(112,519)(113,555)(114,554)(115,553)(116,552)(117,551)(118,550)(119,549)(120,548)(121,547)(122,546)(123,545)(124,544)(125,543)(126,542)(127,541)(128,540)(129,539)(130,538)(131,537)(132,536)(133,535)(134,534)(135,533)(136,532)(137,531)(138,530)(139,529)(140,528)(141,527)(142,526)(143,525)(144,524)(145,523)(146,522)(147,521)(148,520)(149,297)(150,333)(151,332)(152,331)(153,330)(154,329)(155,328)(156,327)(157,326)(158,325)(159,324)(160,323)(161,322)(162,321)(163,320)(164,319)(165,318)(166,317)(167,316)(168,315)(169,314)(170,313)(171,312)(172,311)(173,310)(174,309)(175,308)(176,307)(177,306)(178,305)(179,304)(180,303)(181,302)(182,301)(183,300)(184,299)(185,298)(186,334)(187,370)(188,369)(189,368)(190,367)(191,366)(192,365)(193,364)(194,363)(195,362)(196,361)(197,360)(198,359)(199,358)(200,357)(201,356)(202,355)(203,354)(204,353)(205,352)(206,351)(207,350)(208,349)(209,348)(210,347)(211,346)(212,345)(213,344)(214,343)(215,342)(216,341)(217,340)(218,339)(219,338)(220,337)(221,336)(222,335)(223,408)(224,444)(225,443)(226,442)(227,441)(228,440)(229,439)(230,438)(231,437)(232,436)(233,435)(234,434)(235,433)(236,432)(237,431)(238,430)(239,429)(240,428)(241,427)(242,426)(243,425)(244,424)(245,423)(246,422)(247,421)(248,420)(249,419)(250,418)(251,417)(252,416)(253,415)(254,414)(255,413)(256,412)(257,411)(258,410)(259,409)(260,371)(261,407)(262,406)(263,405)(264,404)(265,403)(266,402)(267,401)(268,400)(269,399)(270,398)(271,397)(272,396)(273,395)(274,394)(275,393)(276,392)(277,391)(278,390)(279,389)(280,388)(281,387)(282,386)(283,385)(284,384)(285,383)(286,382)(287,381)(288,380)(289,379)(290,378)(291,377)(292,376)(293,375)(294,374)(295,373)(296,372);
s2 := Sym(592)!(  1,150)(  2,149)(  3,185)(  4,184)(  5,183)(  6,182)(  7,181)(  8,180)(  9,179)( 10,178)( 11,177)( 12,176)( 13,175)( 14,174)( 15,173)( 16,172)( 17,171)( 18,170)( 19,169)( 20,168)( 21,167)( 22,166)( 23,165)( 24,164)( 25,163)( 26,162)( 27,161)( 28,160)( 29,159)( 30,158)( 31,157)( 32,156)( 33,155)( 34,154)( 35,153)( 36,152)( 37,151)( 38,187)( 39,186)( 40,222)( 41,221)( 42,220)( 43,219)( 44,218)( 45,217)( 46,216)( 47,215)( 48,214)( 49,213)( 50,212)( 51,211)( 52,210)( 53,209)( 54,208)( 55,207)( 56,206)( 57,205)( 58,204)( 59,203)( 60,202)( 61,201)( 62,200)( 63,199)( 64,198)( 65,197)( 66,196)( 67,195)( 68,194)( 69,193)( 70,192)( 71,191)( 72,190)( 73,189)( 74,188)( 75,224)( 76,223)( 77,259)( 78,258)( 79,257)( 80,256)( 81,255)( 82,254)( 83,253)( 84,252)( 85,251)( 86,250)( 87,249)( 88,248)( 89,247)( 90,246)( 91,245)( 92,244)( 93,243)( 94,242)( 95,241)( 96,240)( 97,239)( 98,238)( 99,237)(100,236)(101,235)(102,234)(103,233)(104,232)(105,231)(106,230)(107,229)(108,228)(109,227)(110,226)(111,225)(112,261)(113,260)(114,296)(115,295)(116,294)(117,293)(118,292)(119,291)(120,290)(121,289)(122,288)(123,287)(124,286)(125,285)(126,284)(127,283)(128,282)(129,281)(130,280)(131,279)(132,278)(133,277)(134,276)(135,275)(136,274)(137,273)(138,272)(139,271)(140,270)(141,269)(142,268)(143,267)(144,266)(145,265)(146,264)(147,263)(148,262)(297,446)(298,445)(299,481)(300,480)(301,479)(302,478)(303,477)(304,476)(305,475)(306,474)(307,473)(308,472)(309,471)(310,470)(311,469)(312,468)(313,467)(314,466)(315,465)(316,464)(317,463)(318,462)(319,461)(320,460)(321,459)(322,458)(323,457)(324,456)(325,455)(326,454)(327,453)(328,452)(329,451)(330,450)(331,449)(332,448)(333,447)(334,483)(335,482)(336,518)(337,517)(338,516)(339,515)(340,514)(341,513)(342,512)(343,511)(344,510)(345,509)(346,508)(347,507)(348,506)(349,505)(350,504)(351,503)(352,502)(353,501)(354,500)(355,499)(356,498)(357,497)(358,496)(359,495)(360,494)(361,493)(362,492)(363,491)(364,490)(365,489)(366,488)(367,487)(368,486)(369,485)(370,484)(371,520)(372,519)(373,555)(374,554)(375,553)(376,552)(377,551)(378,550)(379,549)(380,548)(381,547)(382,546)(383,545)(384,544)(385,543)(386,542)(387,541)(388,540)(389,539)(390,538)(391,537)(392,536)(393,535)(394,534)(395,533)(396,532)(397,531)(398,530)(399,529)(400,528)(401,527)(402,526)(403,525)(404,524)(405,523)(406,522)(407,521)(408,557)(409,556)(410,592)(411,591)(412,590)(413,589)(414,588)(415,587)(416,586)(417,585)(418,584)(419,583)(420,582)(421,581)(422,580)(423,579)(424,578)(425,577)(426,576)(427,575)(428,574)(429,573)(430,572)(431,571)(432,570)(433,569)(434,568)(435,567)(436,566)(437,565)(438,564)(439,563)(440,562)(441,561)(442,560)(443,559)(444,558);
poly := sub<Sym(592)|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, 
s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*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