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