Polytope of Type {240,4}

Play with this polytope as a twisty puzzle

s0 := (  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)
( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)( 99,108)(100,107)(121,181)(122,182)(123,184)(124,183)(125,197)(126,198)(127,200)(128,199)(129,193)(130,194)(131,196)(132,195)(133,189)(134,190)(135,192)(136,191)(137,185)(138,186)(139,188)(140,187)(141,221)(142,222)(143,224)(144,223)(145,237)(146,238)(147,240)(148,239)(149,233)(150,234)(151,236)(152,235)(153,229)(154,230)(155,232)(156,231)(157,225)(158,226)(159,228)(160,227)(161,201)(162,202)(163,204)(164,203)(165,217)(166,218)(167,220)(168,219)(169,213)(170,214)(171,216)(172,215)(173,209)(174,210)(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(241,361)(242,362)(243,364)(244,363)(245,377)(246,378)(247,380)(248,379)(249,373)(250,374)(251,376)(252,375)(253,369)(254,370)(255,372)(256,371)(257,365)(258,366)(259,368)(260,367)(261,401)(262,402)(263,404)(264,403)(265,417)(266,418)(267,420)(268,419)(269,413)(270,414)(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)(278,406)(279,408)(280,407)(281,381)(282,382)(283,384)(284,383)(285,397)(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,421)(302,422)(303,424)(304,423)(305,437)(306,438)(307,440)(308,439)(309,433)(310,434)(311,436)(312,435)(313,429)(314,430)(315,432)(316,431)(317,425)(318,426)(319,428)(320,427)(321,461)(322,462)(323,464)(324,463)(325,477)(326,478)(327,480)(328,479)(329,473)(330,474)(331,476)(332,475)(333,469)(334,470)(335,472)(336,471)(337,465)(338,466)(339,468)(340,467)(341,441)(342,442)(343,444)(344,443)(345,457)(346,458)(347,460)(348,459)(349,453)(350,454)(351,456)(352,455)(353,449)(354,450)(355,452)(356,451)(357,445)(358,446)(359,448)(360,447)(481,721)(482,722)(483,724)(484,723)(485,737)(486,738)(487,740)(488,739)(489,733)(490,734)(491,736)(492,735)(493,729)(494,730)(495,732)(496,731)(497,725)(498,726)(499,728)(500,727)(501,761)(502,762)(503,764)(504,763)(505,777)(506,778)(507,780)(508,779)(509,773)(510,774)(511,776)(512,775)(513,769)(514,770)(515,772)(516,771)(517,765)(518,766)(519,768)(520,767)(521,741)(522,742)(523,744)(524,743)(525,757)(526,758)(527,760)(528,759)(529,753)(530,754)(531,756)(532,755)(533,749)(534,750)(535,752)(536,751)(537,745)(538,746)(539,748)(540,747)(541,781)(542,782)(543,784)(544,783)(545,797)(546,798)(547,800)(548,799)(549,793)(550,794)(551,796)(552,795)(553,789)(554,790)(555,792)(556,791)(557,785)(558,786)(559,788)(560,787)(561,821)(562,822)(563,824)(564,823)(565,837)(566,838)(567,840)(568,839)(569,833)(570,834)(571,836)(572,835)(573,829)(574,830)(575,832)(576,831)(577,825)(578,826)(579,828)(580,827)(581,801)(582,802)(583,804)(584,803)(585,817)(586,818)(587,820)(588,819)(589,813)(590,814)(591,816)(592,815)(593,809)(594,810)(595,812)(596,811)(597,805)(598,806)(599,808)(600,807)(601,901)(602,902)(603,904)(604,903)(605,917)(606,918)(607,920)(608,919)(609,913)(610,914)(611,916)(612,915)(613,909)(614,910)(615,912)(616,911)(617,905)(618,906)(619,908)(620,907)(621,941)(622,942)(623,944)(624,943)(625,957)(626,958)(627,960)(628,959)(629,953)(630,954)(631,956)(632,955)(633,949)(634,950)(635,952)(636,951)(637,945)(638,946)(639,948)(640,947)(641,921)(642,922)(643,924)(644,923)(645,937)(646,938)(647,940)(648,939)(649,933)(650,934)(651,936)(652,935)(653,929)(654,930)(655,932)(656,931)(657,925)(658,926)(659,928)(660,927)(661,841)(662,842)(663,844)(664,843)(665,857)(666,858)(667,860)(668,859)(669,853)(670,854)(671,856)(672,855)(673,849)(674,850)(675,852)(676,851)(677,845)(678,846)(679,848)(680,847)(681,881)(682,882)(683,884)(684,883)(685,897)(686,898)(687,900)(688,899)(689,893)(690,894)(691,896)(692,895)(693,889)(694,890)(695,892)(696,891)(697,885)(698,886)(699,888)(700,887)(701,861)(702,862)(703,864)(704,863)(705,877)(706,878)(707,880)(708,879)(709,873)(710,874)(711,876)(712,875)(713,869)(714,870)(715,872)(716,871)
(717,865)(718,866)(719,868)(720,867);;
s1 := (  1,505)(  2,508)(  3,507)(  4,506)(  5,501)(  6,504)(  7,503)(  8,502)(  9,517)( 10,520)( 11,519)( 12,518)( 13,513)( 14,516)( 15,515)( 16,514)( 17,509)( 18,512)( 19,511)( 20,510)
( 21,485)( 22,488)( 23,487)( 24,486)( 25,481)( 26,484)( 27,483)( 28,482)( 29,497)( 30,500)( 31,499)( 32,498)( 33,493)( 34,496)( 35,495)( 36,494)( 37,489)( 38,492)( 39,491)( 40,490)( 41,525)( 42,528)( 43,527)( 44,526)( 45,521)( 46,524)( 47,523)( 48,522)( 49,537)( 50,540)( 51,539)( 52,538)( 53,533)( 54,536)( 55,535)( 56,534)( 57,529)( 58,532)( 59,531)( 60,530)( 61,565)( 62,568)( 63,567)( 64,566)( 65,561)( 66,564)( 67,563)( 68,562)( 69,577)( 70,580)( 71,579)( 72,578)( 73,573)( 74,576)( 75,575)( 76,574)( 77,569)( 78,572)( 79,571)( 80,570)( 81,545)( 82,548)( 83,547)( 84,546)( 85,541)( 86,544)( 87,543)( 88,542)( 89,557)( 90,560)( 91,559)( 92,558)( 93,553)( 94,556)( 95,555)( 96,554)( 97,549)( 98,552)( 99,551)(100,550)(101,585)(102,588)(103,587)(104,586)(105,581)(106,584)(107,583)(108,582)(109,597)(110,600)(111,599)(112,598)(113,593)(114,596)(115,595)(116,594)(117,589)(118,592)(119,591)(120,590)(121,685)(122,688)(123,687)(124,686)(125,681)(126,684)(127,683)(128,682)(129,697)(130,700)(131,699)(132,698)(133,693)(134,696)(135,695)(136,694)(137,689)(138,692)(139,691)(140,690)(141,665)(142,668)(143,667)(144,666)(145,661)(146,664)(147,663)(148,662)(149,677)(150,680)(151,679)(152,678)(153,673)(154,676)(155,675)(156,674)(157,669)(158,672)(159,671)(160,670)(161,705)(162,708)(163,707)(164,706)(165,701)(166,704)(167,703)(168,702)(169,717)(170,720)(171,719)(172,718)(173,713)(174,716)(175,715)(176,714)(177,709)(178,712)(179,711)(180,710)(181,625)(182,628)(183,627)(184,626)(185,621)(186,624)(187,623)(188,622)(189,637)(190,640)(191,639)(192,638)(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)(200,630)(201,605)(202,608)(203,607)(204,606)(205,601)(206,604)(207,603)(208,602)(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)(216,614)(217,609)(218,612)(219,611)(220,610)(221,645)(222,648)(223,647)(224,646)(225,641)(226,644)(227,643)(228,642)(229,657)(230,660)(231,659)(232,658)(233,653)(234,656)(235,655)(236,654)(237,649)(238,652)(239,651)(240,650)(241,865)(242,868)(243,867)(244,866)(245,861)(246,864)(247,863)(248,862)(249,877)(250,880)(251,879)(252,878)(253,873)(254,876)(255,875)(256,874)(257,869)(258,872)(259,871)(260,870)(261,845)(262,848)(263,847)(264,846)(265,841)(266,844)(267,843)(268,842)(269,857)(270,860)(271,859)(272,858)(273,853)(274,856)(275,855)(276,854)(277,849)(278,852)(279,851)(280,850)(281,885)(282,888)(283,887)(284,886)(285,881)(286,884)(287,883)(288,882)(289,897)(290,900)(291,899)(292,898)(293,893)(294,896)(295,895)(296,894)(297,889)(298,892)(299,891)(300,890)(301,925)(302,928)(303,927)(304,926)(305,921)(306,924)(307,923)(308,922)(309,937)(310,940)(311,939)(312,938)(313,933)(314,936)(315,935)(316,934)(317,929)(318,932)(319,931)(320,930)(321,905)(322,908)(323,907)(324,906)(325,901)(326,904)(327,903)(328,902)(329,917)(330,920)(331,919)(332,918)(333,913)(334,916)(335,915)(336,914)(337,909)(338,912)(339,911)(340,910)(341,945)(342,948)(343,947)(344,946)(345,941)(346,944)(347,943)(348,942)(349,957)(350,960)(351,959)(352,958)(353,953)(354,956)(355,955)(356,954)(357,949)(358,952)(359,951)(360,950)(361,745)(362,748)(363,747)(364,746)(365,741)(366,744)(367,743)(368,742)(369,757)(370,760)(371,759)(372,758)(373,753)(374,756)(375,755)(376,754)(377,749)(378,752)(379,751)(380,750)(381,725)(382,728)(383,727)(384,726)(385,721)(386,724)(387,723)(388,722)(389,737)(390,740)(391,739)(392,738)(393,733)(394,736)(395,735)(396,734)(397,729)(398,732)(399,731)(400,730)(401,765)(402,768)(403,767)(404,766)(405,761)(406,764)(407,763)(408,762)(409,777)(410,780)(411,779)(412,778)(413,773)(414,776)(415,775)(416,774)(417,769)(418,772)(419,771)(420,770)(421,805)(422,808)(423,807)(424,806)(425,801)(426,804)(427,803)(428,802)(429,817)(430,820)(431,819)(432,818)(433,813)(434,816)(435,815)(436,814)(437,809)(438,812)(439,811)(440,810)(441,785)(442,788)(443,787)(444,786)(445,781)(446,784)(447,783)(448,782)(449,797)(450,800)(451,799)(452,798)(453,793)(454,796)(455,795)(456,794)(457,789)(458,792)(459,791)(460,790)(461,825)(462,828)(463,827)(464,826)(465,821)(466,824)(467,823)(468,822)(469,837)(470,840)(471,839)(472,838)(473,833)(474,836)
(475,835)(476,834)(477,829)(478,832)(479,831)(480,830);;
s2 := (  1, 62)(  2, 61)(  3, 64)(  4, 63)(  5, 66)(  6, 65)(  7, 68)(  8, 67)(  9, 70)( 10, 69)( 11, 72)( 12, 71)( 13, 74)( 14, 73)( 15, 76)( 16, 75)( 17, 78)( 18, 77)( 19, 80)( 20, 79)
( 21, 82)( 22, 81)( 23, 84)( 24, 83)( 25, 86)( 26, 85)( 27, 88)( 28, 87)( 29, 90)( 30, 89)( 31, 92)( 32, 91)( 33, 94)( 34, 93)( 35, 96)( 36, 95)( 37, 98)( 38, 97)( 39,100)( 40, 99)( 41,102)( 42,101)( 43,104)( 44,103)( 45,106)( 46,105)( 47,108)( 48,107)( 49,110)( 50,109)( 51,112)( 52,111)( 53,114)( 54,113)( 55,116)( 56,115)( 57,118)( 58,117)( 59,120)( 60,119)(121,182)(122,181)(123,184)(124,183)(125,186)(126,185)(127,188)(128,187)(129,190)(130,189)(131,192)(132,191)(133,194)(134,193)(135,196)(136,195)(137,198)(138,197)(139,200)(140,199)(141,202)(142,201)(143,204)(144,203)(145,206)(146,205)(147,208)(148,207)(149,210)(150,209)(151,212)(152,211)(153,214)(154,213)(155,216)(156,215)(157,218)(158,217)(159,220)(160,219)(161,222)(162,221)(163,224)(164,223)(165,226)(166,225)(167,228)(168,227)(169,230)(170,229)(171,232)(172,231)(173,234)(174,233)(175,236)(176,235)(177,238)(178,237)(179,240)(180,239)(241,302)(242,301)(243,304)(244,303)(245,306)(246,305)(247,308)(248,307)(249,310)(250,309)(251,312)(252,311)(253,314)(254,313)(255,316)(256,315)(257,318)(258,317)(259,320)(260,319)(261,322)(262,321)(263,324)(264,323)(265,326)(266,325)(267,328)(268,327)(269,330)(270,329)(271,332)(272,331)(273,334)(274,333)(275,336)(276,335)(277,338)(278,337)(279,340)(280,339)(281,342)(282,341)(283,344)(284,343)(285,346)(286,345)(287,348)(288,347)(289,350)(290,349)(291,352)(292,351)(293,354)(294,353)(295,356)(296,355)(297,358)(298,357)(299,360)(300,359)(361,422)(362,421)(363,424)(364,423)(365,426)(366,425)(367,428)(368,427)(369,430)(370,429)(371,432)(372,431)(373,434)(374,433)(375,436)(376,435)(377,438)(378,437)(379,440)(380,439)(381,442)(382,441)(383,444)(384,443)(385,446)(386,445)(387,448)(388,447)(389,450)(390,449)(391,452)(392,451)(393,454)(394,453)(395,456)(396,455)(397,458)(398,457)(399,460)(400,459)(401,462)(402,461)(403,464)(404,463)(405,466)(406,465)(407,468)(408,467)(409,470)(410,469)(411,472)(412,471)(413,474)(414,473)(415,476)(416,475)(417,478)(418,477)(419,480)(420,479)(481,542)(482,541)(483,544)(484,543)(485,546)(486,545)(487,548)(488,547)(489,550)(490,549)(491,552)(492,551)(493,554)(494,553)(495,556)(496,555)(497,558)(498,557)(499,560)(500,559)(501,562)(502,561)(503,564)(504,563)(505,566)(506,565)(507,568)(508,567)(509,570)(510,569)(511,572)(512,571)(513,574)(514,573)(515,576)(516,575)(517,578)(518,577)(519,580)(520,579)(521,582)(522,581)(523,584)(524,583)(525,586)(526,585)(527,588)(528,587)(529,590)(530,589)(531,592)(532,591)(533,594)(534,593)(535,596)(536,595)(537,598)(538,597)(539,600)(540,599)(601,662)(602,661)(603,664)(604,663)(605,666)(606,665)(607,668)(608,667)(609,670)(610,669)(611,672)(612,671)(613,674)(614,673)(615,676)(616,675)(617,678)(618,677)(619,680)(620,679)(621,682)(622,681)(623,684)(624,683)(625,686)(626,685)(627,688)(628,687)(629,690)(630,689)(631,692)(632,691)(633,694)(634,693)(635,696)(636,695)(637,698)(638,697)(639,700)(640,699)(641,702)(642,701)(643,704)(644,703)(645,706)(646,705)(647,708)(648,707)(649,710)(650,709)(651,712)(652,711)(653,714)(654,713)(655,716)(656,715)(657,718)(658,717)(659,720)(660,719)(721,782)(722,781)(723,784)(724,783)(725,786)(726,785)(727,788)(728,787)(729,790)(730,789)(731,792)(732,791)(733,794)(734,793)(735,796)(736,795)(737,798)(738,797)(739,800)(740,799)(741,802)(742,801)(743,804)(744,803)(745,806)(746,805)(747,808)(748,807)(749,810)(750,809)(751,812)(752,811)(753,814)(754,813)(755,816)(756,815)(757,818)(758,817)(759,820)(760,819)(761,822)(762,821)(763,824)(764,823)(765,826)(766,825)(767,828)(768,827)(769,830)(770,829)(771,832)(772,831)(773,834)(774,833)(775,836)(776,835)(777,838)(778,837)(779,840)(780,839)(841,902)(842,901)(843,904)(844,903)(845,906)(846,905)(847,908)(848,907)(849,910)(850,909)(851,912)(852,911)(853,914)(854,913)(855,916)(856,915)(857,918)(858,917)(859,920)(860,919)(861,922)(862,921)(863,924)(864,923)(865,926)(866,925)(867,928)(868,927)(869,930)(870,929)(871,932)(872,931)(873,934)(874,933)(875,936)(876,935)(877,938)(878,937)(879,940)(880,939)(881,942)(882,941)(883,944)(884,943)(885,946)(886,945)(887,948)(888,947)(889,950)(890,949)(891,952)(892,951)(893,954)(894,953)
(895,956)(896,955)(897,958)(898,957)(899,960)(900,959);;
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*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*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(960)!(  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)
( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 63, 64)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)( 81,101)( 82,102)( 83,104)( 84,103)( 85,117)( 86,118)( 87,120)( 88,119)( 89,113)( 90,114)( 91,116)( 92,115)( 93,109)( 94,110)( 95,112)( 96,111)( 97,105)( 98,106)( 99,108)(100,107)(121,181)(122,182)(123,184)(124,183)(125,197)(126,198)(127,200)(128,199)(129,193)(130,194)(131,196)(132,195)(133,189)(134,190)(135,192)(136,191)(137,185)(138,186)(139,188)(140,187)(141,221)(142,222)(143,224)(144,223)(145,237)(146,238)(147,240)(148,239)(149,233)(150,234)(151,236)(152,235)(153,229)(154,230)(155,232)(156,231)(157,225)(158,226)(159,228)(160,227)(161,201)(162,202)(163,204)(164,203)(165,217)(166,218)(167,220)(168,219)(169,213)(170,214)(171,216)(172,215)(173,209)(174,210)(175,212)(176,211)(177,205)(178,206)(179,208)(180,207)(241,361)(242,362)(243,364)(244,363)(245,377)(246,378)(247,380)(248,379)(249,373)(250,374)(251,376)(252,375)(253,369)(254,370)(255,372)(256,371)(257,365)(258,366)(259,368)(260,367)(261,401)(262,402)(263,404)(264,403)(265,417)(266,418)(267,420)(268,419)(269,413)(270,414)(271,416)(272,415)(273,409)(274,410)(275,412)(276,411)(277,405)(278,406)(279,408)(280,407)(281,381)(282,382)(283,384)(284,383)(285,397)(286,398)(287,400)(288,399)(289,393)(290,394)(291,396)(292,395)(293,389)(294,390)(295,392)(296,391)(297,385)(298,386)(299,388)(300,387)(301,421)(302,422)(303,424)(304,423)(305,437)(306,438)(307,440)(308,439)(309,433)(310,434)(311,436)(312,435)(313,429)(314,430)(315,432)(316,431)(317,425)(318,426)(319,428)(320,427)(321,461)(322,462)(323,464)(324,463)(325,477)(326,478)(327,480)(328,479)(329,473)(330,474)(331,476)(332,475)(333,469)(334,470)(335,472)(336,471)(337,465)(338,466)(339,468)(340,467)(341,441)(342,442)(343,444)(344,443)(345,457)(346,458)(347,460)(348,459)(349,453)(350,454)(351,456)(352,455)(353,449)(354,450)(355,452)(356,451)(357,445)(358,446)(359,448)(360,447)(481,721)(482,722)(483,724)(484,723)(485,737)(486,738)(487,740)(488,739)(489,733)(490,734)(491,736)(492,735)(493,729)(494,730)(495,732)(496,731)(497,725)(498,726)(499,728)(500,727)(501,761)(502,762)(503,764)(504,763)(505,777)(506,778)(507,780)(508,779)(509,773)(510,774)(511,776)(512,775)(513,769)(514,770)(515,772)(516,771)(517,765)(518,766)(519,768)(520,767)(521,741)(522,742)(523,744)(524,743)(525,757)(526,758)(527,760)(528,759)(529,753)(530,754)(531,756)(532,755)(533,749)(534,750)(535,752)(536,751)(537,745)(538,746)(539,748)(540,747)(541,781)(542,782)(543,784)(544,783)(545,797)(546,798)(547,800)(548,799)(549,793)(550,794)(551,796)(552,795)(553,789)(554,790)(555,792)(556,791)(557,785)(558,786)(559,788)(560,787)(561,821)(562,822)(563,824)(564,823)(565,837)(566,838)(567,840)(568,839)(569,833)(570,834)(571,836)(572,835)(573,829)(574,830)(575,832)(576,831)(577,825)(578,826)(579,828)(580,827)(581,801)(582,802)(583,804)(584,803)(585,817)(586,818)(587,820)(588,819)(589,813)(590,814)(591,816)(592,815)(593,809)(594,810)(595,812)(596,811)(597,805)(598,806)(599,808)(600,807)(601,901)(602,902)(603,904)(604,903)(605,917)(606,918)(607,920)(608,919)(609,913)(610,914)(611,916)(612,915)(613,909)(614,910)(615,912)(616,911)(617,905)(618,906)(619,908)(620,907)(621,941)(622,942)(623,944)(624,943)(625,957)(626,958)(627,960)(628,959)(629,953)(630,954)(631,956)(632,955)(633,949)(634,950)(635,952)(636,951)(637,945)(638,946)(639,948)(640,947)(641,921)(642,922)(643,924)(644,923)(645,937)(646,938)(647,940)(648,939)(649,933)(650,934)(651,936)(652,935)(653,929)(654,930)(655,932)(656,931)(657,925)(658,926)(659,928)(660,927)(661,841)(662,842)(663,844)(664,843)(665,857)(666,858)(667,860)(668,859)(669,853)(670,854)(671,856)(672,855)(673,849)(674,850)(675,852)(676,851)(677,845)(678,846)(679,848)(680,847)(681,881)(682,882)(683,884)(684,883)(685,897)(686,898)(687,900)(688,899)(689,893)(690,894)(691,896)(692,895)(693,889)(694,890)(695,892)(696,891)(697,885)(698,886)(699,888)(700,887)(701,861)(702,862)(703,864)(704,863)(705,877)(706,878)(707,880)(708,879)(709,873)(710,874)(711,876)(712,875)(713,869)(714,870)(715,872)
(716,871)(717,865)(718,866)(719,868)(720,867);
s1 := Sym(960)!(  1,505)(  2,508)(  3,507)(  4,506)(  5,501)(  6,504)(  7,503)(  8,502)(  9,517)( 10,520)( 11,519)( 12,518)( 13,513)( 14,516)( 15,515)( 16,514)( 17,509)( 18,512)( 19,511)
( 20,510)( 21,485)( 22,488)( 23,487)( 24,486)( 25,481)( 26,484)( 27,483)( 28,482)( 29,497)( 30,500)( 31,499)( 32,498)( 33,493)( 34,496)( 35,495)( 36,494)( 37,489)( 38,492)( 39,491)( 40,490)( 41,525)( 42,528)( 43,527)( 44,526)( 45,521)( 46,524)( 47,523)( 48,522)( 49,537)( 50,540)( 51,539)( 52,538)( 53,533)( 54,536)( 55,535)( 56,534)( 57,529)( 58,532)( 59,531)( 60,530)( 61,565)( 62,568)( 63,567)( 64,566)( 65,561)( 66,564)( 67,563)( 68,562)( 69,577)( 70,580)( 71,579)( 72,578)( 73,573)( 74,576)( 75,575)( 76,574)( 77,569)( 78,572)( 79,571)( 80,570)( 81,545)( 82,548)( 83,547)( 84,546)( 85,541)( 86,544)( 87,543)( 88,542)( 89,557)( 90,560)( 91,559)( 92,558)( 93,553)( 94,556)( 95,555)( 96,554)( 97,549)( 98,552)( 99,551)(100,550)(101,585)(102,588)(103,587)(104,586)(105,581)(106,584)(107,583)(108,582)(109,597)(110,600)(111,599)(112,598)(113,593)(114,596)(115,595)(116,594)(117,589)(118,592)(119,591)(120,590)(121,685)(122,688)(123,687)(124,686)(125,681)(126,684)(127,683)(128,682)(129,697)(130,700)(131,699)(132,698)(133,693)(134,696)(135,695)(136,694)(137,689)(138,692)(139,691)(140,690)(141,665)(142,668)(143,667)(144,666)(145,661)(146,664)(147,663)(148,662)(149,677)(150,680)(151,679)(152,678)(153,673)(154,676)(155,675)(156,674)(157,669)(158,672)(159,671)(160,670)(161,705)(162,708)(163,707)(164,706)(165,701)(166,704)(167,703)(168,702)(169,717)(170,720)(171,719)(172,718)(173,713)(174,716)(175,715)(176,714)(177,709)(178,712)(179,711)(180,710)(181,625)(182,628)(183,627)(184,626)(185,621)(186,624)(187,623)(188,622)(189,637)(190,640)(191,639)(192,638)(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)(200,630)(201,605)(202,608)(203,607)(204,606)(205,601)(206,604)(207,603)(208,602)(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)(216,614)(217,609)(218,612)(219,611)(220,610)(221,645)(222,648)(223,647)(224,646)(225,641)(226,644)(227,643)(228,642)(229,657)(230,660)(231,659)(232,658)(233,653)(234,656)(235,655)(236,654)(237,649)(238,652)(239,651)(240,650)(241,865)(242,868)(243,867)(244,866)(245,861)(246,864)(247,863)(248,862)(249,877)(250,880)(251,879)(252,878)(253,873)(254,876)(255,875)(256,874)(257,869)(258,872)(259,871)(260,870)(261,845)(262,848)(263,847)(264,846)(265,841)(266,844)(267,843)(268,842)(269,857)(270,860)(271,859)(272,858)(273,853)(274,856)(275,855)(276,854)(277,849)(278,852)(279,851)(280,850)(281,885)(282,888)(283,887)(284,886)(285,881)(286,884)(287,883)(288,882)(289,897)(290,900)(291,899)(292,898)(293,893)(294,896)(295,895)(296,894)(297,889)(298,892)(299,891)(300,890)(301,925)(302,928)(303,927)(304,926)(305,921)(306,924)(307,923)(308,922)(309,937)(310,940)(311,939)(312,938)(313,933)(314,936)(315,935)(316,934)(317,929)(318,932)(319,931)(320,930)(321,905)(322,908)(323,907)(324,906)(325,901)(326,904)(327,903)(328,902)(329,917)(330,920)(331,919)(332,918)(333,913)(334,916)(335,915)(336,914)(337,909)(338,912)(339,911)(340,910)(341,945)(342,948)(343,947)(344,946)(345,941)(346,944)(347,943)(348,942)(349,957)(350,960)(351,959)(352,958)(353,953)(354,956)(355,955)(356,954)(357,949)(358,952)(359,951)(360,950)(361,745)(362,748)(363,747)(364,746)(365,741)(366,744)(367,743)(368,742)(369,757)(370,760)(371,759)(372,758)(373,753)(374,756)(375,755)(376,754)(377,749)(378,752)(379,751)(380,750)(381,725)(382,728)(383,727)(384,726)(385,721)(386,724)(387,723)(388,722)(389,737)(390,740)(391,739)(392,738)(393,733)(394,736)(395,735)(396,734)(397,729)(398,732)(399,731)(400,730)(401,765)(402,768)(403,767)(404,766)(405,761)(406,764)(407,763)(408,762)(409,777)(410,780)(411,779)(412,778)(413,773)(414,776)(415,775)(416,774)(417,769)(418,772)(419,771)(420,770)(421,805)(422,808)(423,807)(424,806)(425,801)(426,804)(427,803)(428,802)(429,817)(430,820)(431,819)(432,818)(433,813)(434,816)(435,815)(436,814)(437,809)(438,812)(439,811)(440,810)(441,785)(442,788)(443,787)(444,786)(445,781)(446,784)(447,783)(448,782)(449,797)(450,800)(451,799)(452,798)(453,793)(454,796)(455,795)(456,794)(457,789)(458,792)(459,791)(460,790)(461,825)(462,828)(463,827)(464,826)(465,821)(466,824)(467,823)(468,822)(469,837)(470,840)(471,839)(472,838)(473,833)
(474,836)(475,835)(476,834)(477,829)(478,832)(479,831)(480,830);
s2 := Sym(960)!(  1, 62)(  2, 61)(  3, 64)(  4, 63)(  5, 66)(  6, 65)(  7, 68)(  8, 67)(  9, 70)( 10, 69)( 11, 72)( 12, 71)( 13, 74)( 14, 73)( 15, 76)( 16, 75)( 17, 78)( 18, 77)( 19, 80)
( 20, 79)( 21, 82)( 22, 81)( 23, 84)( 24, 83)( 25, 86)( 26, 85)( 27, 88)( 28, 87)( 29, 90)( 30, 89)( 31, 92)( 32, 91)( 33, 94)( 34, 93)( 35, 96)( 36, 95)( 37, 98)( 38, 97)( 39,100)( 40, 99)( 41,102)( 42,101)( 43,104)( 44,103)( 45,106)( 46,105)( 47,108)( 48,107)( 49,110)( 50,109)( 51,112)( 52,111)( 53,114)( 54,113)( 55,116)( 56,115)( 57,118)( 58,117)( 59,120)( 60,119)(121,182)(122,181)(123,184)(124,183)(125,186)(126,185)(127,188)(128,187)(129,190)(130,189)(131,192)(132,191)(133,194)(134,193)(135,196)(136,195)(137,198)(138,197)(139,200)(140,199)(141,202)(142,201)(143,204)(144,203)(145,206)(146,205)(147,208)(148,207)(149,210)(150,209)(151,212)(152,211)(153,214)(154,213)(155,216)(156,215)(157,218)(158,217)(159,220)(160,219)(161,222)(162,221)(163,224)(164,223)(165,226)(166,225)(167,228)(168,227)(169,230)(170,229)(171,232)(172,231)(173,234)(174,233)(175,236)(176,235)(177,238)(178,237)(179,240)(180,239)(241,302)(242,301)(243,304)(244,303)(245,306)(246,305)(247,308)(248,307)(249,310)(250,309)(251,312)(252,311)(253,314)(254,313)(255,316)(256,315)(257,318)(258,317)(259,320)(260,319)(261,322)(262,321)(263,324)(264,323)(265,326)(266,325)(267,328)(268,327)(269,330)(270,329)(271,332)(272,331)(273,334)(274,333)(275,336)(276,335)(277,338)(278,337)(279,340)(280,339)(281,342)(282,341)(283,344)(284,343)(285,346)(286,345)(287,348)(288,347)(289,350)(290,349)(291,352)(292,351)(293,354)(294,353)(295,356)(296,355)(297,358)(298,357)(299,360)(300,359)(361,422)(362,421)(363,424)(364,423)(365,426)(366,425)(367,428)(368,427)(369,430)(370,429)(371,432)(372,431)(373,434)(374,433)(375,436)(376,435)(377,438)(378,437)(379,440)(380,439)(381,442)(382,441)(383,444)(384,443)(385,446)(386,445)(387,448)(388,447)(389,450)(390,449)(391,452)(392,451)(393,454)(394,453)(395,456)(396,455)(397,458)(398,457)(399,460)(400,459)(401,462)(402,461)(403,464)(404,463)(405,466)(406,465)(407,468)(408,467)(409,470)(410,469)(411,472)(412,471)(413,474)(414,473)(415,476)(416,475)(417,478)(418,477)(419,480)(420,479)(481,542)(482,541)(483,544)(484,543)(485,546)(486,545)(487,548)(488,547)(489,550)(490,549)(491,552)(492,551)(493,554)(494,553)(495,556)(496,555)(497,558)(498,557)(499,560)(500,559)(501,562)(502,561)(503,564)(504,563)(505,566)(506,565)(507,568)(508,567)(509,570)(510,569)(511,572)(512,571)(513,574)(514,573)(515,576)(516,575)(517,578)(518,577)(519,580)(520,579)(521,582)(522,581)(523,584)(524,583)(525,586)(526,585)(527,588)(528,587)(529,590)(530,589)(531,592)(532,591)(533,594)(534,593)(535,596)(536,595)(537,598)(538,597)(539,600)(540,599)(601,662)(602,661)(603,664)(604,663)(605,666)(606,665)(607,668)(608,667)(609,670)(610,669)(611,672)(612,671)(613,674)(614,673)(615,676)(616,675)(617,678)(618,677)(619,680)(620,679)(621,682)(622,681)(623,684)(624,683)(625,686)(626,685)(627,688)(628,687)(629,690)(630,689)(631,692)(632,691)(633,694)(634,693)(635,696)(636,695)(637,698)(638,697)(639,700)(640,699)(641,702)(642,701)(643,704)(644,703)(645,706)(646,705)(647,708)(648,707)(649,710)(650,709)(651,712)(652,711)(653,714)(654,713)(655,716)(656,715)(657,718)(658,717)(659,720)(660,719)(721,782)(722,781)(723,784)(724,783)(725,786)(726,785)(727,788)(728,787)(729,790)(730,789)(731,792)(732,791)(733,794)(734,793)(735,796)(736,795)(737,798)(738,797)(739,800)(740,799)(741,802)(742,801)(743,804)(744,803)(745,806)(746,805)(747,808)(748,807)(749,810)(750,809)(751,812)(752,811)(753,814)(754,813)(755,816)(756,815)(757,818)(758,817)(759,820)(760,819)(761,822)(762,821)(763,824)(764,823)(765,826)(766,825)(767,828)(768,827)(769,830)(770,829)(771,832)(772,831)(773,834)(774,833)(775,836)(776,835)(777,838)(778,837)(779,840)(780,839)(841,902)(842,901)(843,904)(844,903)(845,906)(846,905)(847,908)(848,907)(849,910)(850,909)(851,912)(852,911)(853,914)(854,913)(855,916)(856,915)(857,918)(858,917)(859,920)(860,919)(861,922)(862,921)(863,924)(864,923)(865,926)(866,925)(867,928)(868,927)(869,930)(870,929)(871,932)(872,931)(873,934)(874,933)(875,936)(876,935)(877,938)(878,937)(879,940)(880,939)(881,942)(882,941)(883,944)(884,943)(885,946)(886,945)(887,948)(888,947)(889,950)(890,949)(891,952)(892,951)(893,954)
(894,953)(895,956)(896,955)(897,958)(898,957)(899,960)(900,959);
poly := sub<Sym(960)|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*s1*s0*s1*s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s2*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