Polytope of Type {246,4}

Play with this polytope as a twisty puzzle

s0 := (  3,  4)(  5,161)(  6,162)(  7,164)(  8,163)(  9,157)( 10,158)( 11,160)( 12,159)( 13,153)( 14,154)( 15,156)( 16,155)( 17,149)( 18,150)( 19,152)( 20,151)( 21,145)( 22,146)( 23,148)
( 24,147)( 25,141)( 26,142)( 27,144)( 28,143)( 29,137)( 30,138)( 31,140)( 32,139)( 33,133)( 34,134)( 35,136)( 36,135)( 37,129)( 38,130)( 39,132)( 40,131)( 41,125)( 42,126)( 43,128)( 44,127)( 45,121)( 46,122)( 47,124)( 48,123)( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)( 73, 93)( 74, 94)( 75, 96)( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 81, 85)( 82, 86)( 83, 88)( 84, 87)(165,329)(166,330)(167,332)(168,331)(169,489)(170,490)(171,492)(172,491)(173,485)(174,486)(175,488)(176,487)(177,481)(178,482)(179,484)(180,483)(181,477)(182,478)(183,480)(184,479)(185,473)(186,474)(187,476)(188,475)(189,469)(190,470)(191,472)(192,471)(193,465)(194,466)(195,468)(196,467)(197,461)(198,462)(199,464)(200,463)(201,457)(202,458)(203,460)(204,459)(205,453)(206,454)(207,456)(208,455)(209,449)(210,450)(211,452)(212,451)(213,445)(214,446)(215,448)(216,447)(217,441)(218,442)(219,444)(220,443)(221,437)(222,438)(223,440)(224,439)(225,433)(226,434)(227,436)(228,435)(229,429)(230,430)(231,432)(232,431)(233,425)(234,426)(235,428)(236,427)(237,421)(238,422)(239,424)(240,423)(241,417)(242,418)(243,420)(244,419)(245,413)(246,414)(247,416)(248,415)(249,409)(250,410)(251,412)(252,411)(253,405)(254,406)(255,408)(256,407)(257,401)(258,402)(259,404)(260,403)(261,397)(262,398)(263,400)(264,399)(265,393)(266,394)(267,396)(268,395)(269,389)(270,390)(271,392)(272,391)(273,385)(274,386)(275,388)(276,387)(277,381)(278,382)(279,384)(280,383)(281,377)(282,378)(283,380)(284,379)(285,373)(286,374)(287,376)(288,375)(289,369)(290,370)(291,372)(292,371)(293,365)(294,366)(295,368)(296,367)(297,361)(298,362)(299,364)(300,363)(301,357)(302,358)(303,360)(304,359)(305,353)(306,354)(307,356)(308,355)(309,349)(310,350)(311,352)(312,351)(313,345)(314,346)(315,348)(316,347)(317,341)(318,342)(319,344)(320,343)(321,337)(322,338)(323,340)(324,339)(325,333)(326,334)(327,336)(328,335)(495,496)(497,653)(498,654)(499,656)(500,655)(501,649)(502,650)(503,652)(504,651)(505,645)(506,646)(507,648)(508,647)(509,641)(510,642)(511,644)(512,643)(513,637)(514,638)(515,640)(516,639)(517,633)(518,634)(519,636)(520,635)(521,629)(522,630)(523,632)(524,631)(525,625)(526,626)(527,628)(528,627)(529,621)(530,622)(531,624)(532,623)(533,617)(534,618)(535,620)(536,619)(537,613)(538,614)(539,616)(540,615)(541,609)(542,610)(543,612)(544,611)(545,605)(546,606)(547,608)(548,607)(549,601)(550,602)(551,604)(552,603)(553,597)(554,598)(555,600)(556,599)(557,593)(558,594)(559,596)(560,595)(561,589)(562,590)(563,592)(564,591)(565,585)(566,586)(567,588)(568,587)(569,581)(570,582)(571,584)(572,583)(573,577)(574,578)(575,580)(576,579)(657,821)(658,822)(659,824)(660,823)(661,981)(662,982)(663,984)(664,983)(665,977)(666,978)(667,980)(668,979)(669,973)(670,974)(671,976)(672,975)(673,969)(674,970)(675,972)(676,971)(677,965)(678,966)(679,968)(680,967)(681,961)(682,962)(683,964)(684,963)(685,957)(686,958)(687,960)(688,959)(689,953)(690,954)(691,956)(692,955)(693,949)(694,950)(695,952)(696,951)(697,945)(698,946)(699,948)(700,947)(701,941)(702,942)(703,944)(704,943)(705,937)(706,938)(707,940)(708,939)(709,933)(710,934)(711,936)(712,935)(713,929)(714,930)(715,932)(716,931)(717,925)(718,926)(719,928)(720,927)(721,921)(722,922)(723,924)(724,923)(725,917)(726,918)(727,920)(728,919)(729,913)(730,914)(731,916)(732,915)(733,909)(734,910)(735,912)(736,911)(737,905)(738,906)(739,908)(740,907)(741,901)(742,902)(743,904)(744,903)(745,897)(746,898)(747,900)(748,899)(749,893)(750,894)(751,896)(752,895)(753,889)(754,890)(755,892)(756,891)(757,885)(758,886)(759,888)(760,887)(761,881)(762,882)(763,884)(764,883)(765,877)(766,878)(767,880)(768,879)(769,873)(770,874)(771,876)(772,875)(773,869)(774,870)(775,872)(776,871)(777,865)(778,866)(779,868)(780,867)(781,861)(782,862)(783,864)(784,863)(785,857)(786,858)(787,860)(788,859)(789,853)(790,854)(791,856)(792,855)(793,849)(794,850)(795,852)(796,851)(797,845)(798,846)(799,848)(800,847)(801,841)(802,842)(803,844)(804,843)
(805,837)(806,838)(807,840)(808,839)(809,833)(810,834)(811,836)(812,835)(813,829)(814,830)(815,832)(816,831)(817,825)(818,826)(819,828)(820,827);;
s1 := (  1,661)(  2,664)(  3,663)(  4,662)(  5,657)(  6,660)(  7,659)(  8,658)(  9,817)( 10,820)( 11,819)( 12,818)( 13,813)( 14,816)( 15,815)( 16,814)( 17,809)( 18,812)( 19,811)( 20,810)
( 21,805)( 22,808)( 23,807)( 24,806)( 25,801)( 26,804)( 27,803)( 28,802)( 29,797)( 30,800)( 31,799)( 32,798)( 33,793)( 34,796)( 35,795)( 36,794)( 37,789)( 38,792)( 39,791)( 40,790)( 41,785)( 42,788)( 43,787)( 44,786)( 45,781)( 46,784)( 47,783)( 48,782)( 49,777)( 50,780)( 51,779)( 52,778)( 53,773)( 54,776)( 55,775)( 56,774)( 57,769)( 58,772)( 59,771)( 60,770)( 61,765)( 62,768)( 63,767)( 64,766)( 65,761)( 66,764)( 67,763)( 68,762)( 69,757)( 70,760)( 71,759)( 72,758)( 73,753)( 74,756)( 75,755)( 76,754)( 77,749)( 78,752)( 79,751)( 80,750)( 81,745)( 82,748)( 83,747)( 84,746)( 85,741)( 86,744)( 87,743)( 88,742)( 89,737)( 90,740)( 91,739)( 92,738)( 93,733)( 94,736)( 95,735)( 96,734)( 97,729)( 98,732)( 99,731)(100,730)(101,725)(102,728)(103,727)(104,726)(105,721)(106,724)(107,723)(108,722)(109,717)(110,720)(111,719)(112,718)(113,713)(114,716)(115,715)(116,714)(117,709)(118,712)(119,711)(120,710)(121,705)(122,708)(123,707)(124,706)(125,701)(126,704)(127,703)(128,702)(129,697)(130,700)(131,699)(132,698)(133,693)(134,696)(135,695)(136,694)(137,689)(138,692)(139,691)(140,690)(141,685)(142,688)(143,687)(144,686)(145,681)(146,684)(147,683)(148,682)(149,677)(150,680)(151,679)(152,678)(153,673)(154,676)(155,675)(156,674)(157,669)(158,672)(159,671)(160,670)(161,665)(162,668)(163,667)(164,666)(165,497)(166,500)(167,499)(168,498)(169,493)(170,496)(171,495)(172,494)(173,653)(174,656)(175,655)(176,654)(177,649)(178,652)(179,651)(180,650)(181,645)(182,648)(183,647)(184,646)(185,641)(186,644)(187,643)(188,642)(189,637)(190,640)(191,639)(192,638)(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)(200,630)(201,625)(202,628)(203,627)(204,626)(205,621)(206,624)(207,623)(208,622)(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)(216,614)(217,609)(218,612)(219,611)(220,610)(221,605)(222,608)(223,607)(224,606)(225,601)(226,604)(227,603)(228,602)(229,597)(230,600)(231,599)(232,598)(233,593)(234,596)(235,595)(236,594)(237,589)(238,592)(239,591)(240,590)(241,585)(242,588)(243,587)(244,586)(245,581)(246,584)(247,583)(248,582)(249,577)(250,580)(251,579)(252,578)(253,573)(254,576)(255,575)(256,574)(257,569)(258,572)(259,571)(260,570)(261,565)(262,568)(263,567)(264,566)(265,561)(266,564)(267,563)(268,562)(269,557)(270,560)(271,559)(272,558)(273,553)(274,556)(275,555)(276,554)(277,549)(278,552)(279,551)(280,550)(281,545)(282,548)(283,547)(284,546)(285,541)(286,544)(287,543)(288,542)(289,537)(290,540)(291,539)(292,538)(293,533)(294,536)(295,535)(296,534)(297,529)(298,532)(299,531)(300,530)(301,525)(302,528)(303,527)(304,526)(305,521)(306,524)(307,523)(308,522)(309,517)(310,520)(311,519)(312,518)(313,513)(314,516)(315,515)(316,514)(317,509)(318,512)(319,511)(320,510)(321,505)(322,508)(323,507)(324,506)(325,501)(326,504)(327,503)(328,502)(329,825)(330,828)(331,827)(332,826)(333,821)(334,824)(335,823)(336,822)(337,981)(338,984)(339,983)(340,982)(341,977)(342,980)(343,979)(344,978)(345,973)(346,976)(347,975)(348,974)(349,969)(350,972)(351,971)(352,970)(353,965)(354,968)(355,967)(356,966)(357,961)(358,964)(359,963)(360,962)(361,957)(362,960)(363,959)(364,958)(365,953)(366,956)(367,955)(368,954)(369,949)(370,952)(371,951)(372,950)(373,945)(374,948)(375,947)(376,946)(377,941)(378,944)(379,943)(380,942)(381,937)(382,940)(383,939)(384,938)(385,933)(386,936)(387,935)(388,934)(389,929)(390,932)(391,931)(392,930)(393,925)(394,928)(395,927)(396,926)(397,921)(398,924)(399,923)(400,922)(401,917)(402,920)(403,919)(404,918)(405,913)(406,916)(407,915)(408,914)(409,909)(410,912)(411,911)(412,910)(413,905)(414,908)(415,907)(416,906)(417,901)(418,904)(419,903)(420,902)(421,897)(422,900)(423,899)(424,898)(425,893)(426,896)(427,895)(428,894)(429,889)(430,892)(431,891)(432,890)(433,885)(434,888)(435,887)(436,886)(437,881)(438,884)(439,883)(440,882)(441,877)(442,880)(443,879)(444,878)(445,873)(446,876)(447,875)(448,874)(449,869)(450,872)(451,871)(452,870)(453,865)(454,868)(455,867)(456,866)(457,861)(458,864)(459,863)(460,862)(461,857)(462,860)(463,859)(464,858)(465,853)(466,856)(467,855)(468,854)(469,849)(470,852)(471,851)(472,850)(473,845)(474,848)
(475,847)(476,846)(477,841)(478,844)(479,843)(480,842)(481,837)(482,840)(483,839)(484,838)(485,833)(486,836)(487,835)(488,834)(489,829)(490,832)(491,831)(492,830);;
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)(961,962)(963,964)(965,966)(967,968)(969,970)(971,972)(973,974)(975,976)(977,978)(979,980)(981,982)(983,984);;
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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 ];;
poly := F / rels;;
 

s0 := Sym(984)!(  3,  4)(  5,161)(  6,162)(  7,164)(  8,163)(  9,157)( 10,158)( 11,160)( 12,159)( 13,153)( 14,154)( 15,156)( 16,155)( 17,149)( 18,150)( 19,152)( 20,151)( 21,145)( 22,146)
( 23,148)( 24,147)( 25,141)( 26,142)( 27,144)( 28,143)( 29,137)( 30,138)( 31,140)( 32,139)( 33,133)( 34,134)( 35,136)( 36,135)( 37,129)( 38,130)( 39,132)( 40,131)( 41,125)( 42,126)( 43,128)( 44,127)( 45,121)( 46,122)( 47,124)( 48,123)( 49,117)( 50,118)( 51,120)( 52,119)( 53,113)( 54,114)( 55,116)( 56,115)( 57,109)( 58,110)( 59,112)( 60,111)( 61,105)( 62,106)( 63,108)( 64,107)( 65,101)( 66,102)( 67,104)( 68,103)( 69, 97)( 70, 98)( 71,100)( 72, 99)( 73, 93)( 74, 94)( 75, 96)( 76, 95)( 77, 89)( 78, 90)( 79, 92)( 80, 91)( 81, 85)( 82, 86)( 83, 88)( 84, 87)(165,329)(166,330)(167,332)(168,331)(169,489)(170,490)(171,492)(172,491)(173,485)(174,486)(175,488)(176,487)(177,481)(178,482)(179,484)(180,483)(181,477)(182,478)(183,480)(184,479)(185,473)(186,474)(187,476)(188,475)(189,469)(190,470)(191,472)(192,471)(193,465)(194,466)(195,468)(196,467)(197,461)(198,462)(199,464)(200,463)(201,457)(202,458)(203,460)(204,459)(205,453)(206,454)(207,456)(208,455)(209,449)(210,450)(211,452)(212,451)(213,445)(214,446)(215,448)(216,447)(217,441)(218,442)(219,444)(220,443)(221,437)(222,438)(223,440)(224,439)(225,433)(226,434)(227,436)(228,435)(229,429)(230,430)(231,432)(232,431)(233,425)(234,426)(235,428)(236,427)(237,421)(238,422)(239,424)(240,423)(241,417)(242,418)(243,420)(244,419)(245,413)(246,414)(247,416)(248,415)(249,409)(250,410)(251,412)(252,411)(253,405)(254,406)(255,408)(256,407)(257,401)(258,402)(259,404)(260,403)(261,397)(262,398)(263,400)(264,399)(265,393)(266,394)(267,396)(268,395)(269,389)(270,390)(271,392)(272,391)(273,385)(274,386)(275,388)(276,387)(277,381)(278,382)(279,384)(280,383)(281,377)(282,378)(283,380)(284,379)(285,373)(286,374)(287,376)(288,375)(289,369)(290,370)(291,372)(292,371)(293,365)(294,366)(295,368)(296,367)(297,361)(298,362)(299,364)(300,363)(301,357)(302,358)(303,360)(304,359)(305,353)(306,354)(307,356)(308,355)(309,349)(310,350)(311,352)(312,351)(313,345)(314,346)(315,348)(316,347)(317,341)(318,342)(319,344)(320,343)(321,337)(322,338)(323,340)(324,339)(325,333)(326,334)(327,336)(328,335)(495,496)(497,653)(498,654)(499,656)(500,655)(501,649)(502,650)(503,652)(504,651)(505,645)(506,646)(507,648)(508,647)(509,641)(510,642)(511,644)(512,643)(513,637)(514,638)(515,640)(516,639)(517,633)(518,634)(519,636)(520,635)(521,629)(522,630)(523,632)(524,631)(525,625)(526,626)(527,628)(528,627)(529,621)(530,622)(531,624)(532,623)(533,617)(534,618)(535,620)(536,619)(537,613)(538,614)(539,616)(540,615)(541,609)(542,610)(543,612)(544,611)(545,605)(546,606)(547,608)(548,607)(549,601)(550,602)(551,604)(552,603)(553,597)(554,598)(555,600)(556,599)(557,593)(558,594)(559,596)(560,595)(561,589)(562,590)(563,592)(564,591)(565,585)(566,586)(567,588)(568,587)(569,581)(570,582)(571,584)(572,583)(573,577)(574,578)(575,580)(576,579)(657,821)(658,822)(659,824)(660,823)(661,981)(662,982)(663,984)(664,983)(665,977)(666,978)(667,980)(668,979)(669,973)(670,974)(671,976)(672,975)(673,969)(674,970)(675,972)(676,971)(677,965)(678,966)(679,968)(680,967)(681,961)(682,962)(683,964)(684,963)(685,957)(686,958)(687,960)(688,959)(689,953)(690,954)(691,956)(692,955)(693,949)(694,950)(695,952)(696,951)(697,945)(698,946)(699,948)(700,947)(701,941)(702,942)(703,944)(704,943)(705,937)(706,938)(707,940)(708,939)(709,933)(710,934)(711,936)(712,935)(713,929)(714,930)(715,932)(716,931)(717,925)(718,926)(719,928)(720,927)(721,921)(722,922)(723,924)(724,923)(725,917)(726,918)(727,920)(728,919)(729,913)(730,914)(731,916)(732,915)(733,909)(734,910)(735,912)(736,911)(737,905)(738,906)(739,908)(740,907)(741,901)(742,902)(743,904)(744,903)(745,897)(746,898)(747,900)(748,899)(749,893)(750,894)(751,896)(752,895)(753,889)(754,890)(755,892)(756,891)(757,885)(758,886)(759,888)(760,887)(761,881)(762,882)(763,884)(764,883)(765,877)(766,878)(767,880)(768,879)(769,873)(770,874)(771,876)(772,875)(773,869)(774,870)(775,872)(776,871)(777,865)(778,866)(779,868)(780,867)(781,861)(782,862)(783,864)(784,863)(785,857)(786,858)(787,860)(788,859)(789,853)(790,854)(791,856)(792,855)(793,849)(794,850)(795,852)(796,851)(797,845)(798,846)(799,848)(800,847)(801,841)(802,842)(803,844)
(804,843)(805,837)(806,838)(807,840)(808,839)(809,833)(810,834)(811,836)(812,835)(813,829)(814,830)(815,832)(816,831)(817,825)(818,826)(819,828)(820,827);
s1 := Sym(984)!(  1,661)(  2,664)(  3,663)(  4,662)(  5,657)(  6,660)(  7,659)(  8,658)(  9,817)( 10,820)( 11,819)( 12,818)( 13,813)( 14,816)( 15,815)( 16,814)( 17,809)( 18,812)( 19,811)
( 20,810)( 21,805)( 22,808)( 23,807)( 24,806)( 25,801)( 26,804)( 27,803)( 28,802)( 29,797)( 30,800)( 31,799)( 32,798)( 33,793)( 34,796)( 35,795)( 36,794)( 37,789)( 38,792)( 39,791)( 40,790)( 41,785)( 42,788)( 43,787)( 44,786)( 45,781)( 46,784)( 47,783)( 48,782)( 49,777)( 50,780)( 51,779)( 52,778)( 53,773)( 54,776)( 55,775)( 56,774)( 57,769)( 58,772)( 59,771)( 60,770)( 61,765)( 62,768)( 63,767)( 64,766)( 65,761)( 66,764)( 67,763)( 68,762)( 69,757)( 70,760)( 71,759)( 72,758)( 73,753)( 74,756)( 75,755)( 76,754)( 77,749)( 78,752)( 79,751)( 80,750)( 81,745)( 82,748)( 83,747)( 84,746)( 85,741)( 86,744)( 87,743)( 88,742)( 89,737)( 90,740)( 91,739)( 92,738)( 93,733)( 94,736)( 95,735)( 96,734)( 97,729)( 98,732)( 99,731)(100,730)(101,725)(102,728)(103,727)(104,726)(105,721)(106,724)(107,723)(108,722)(109,717)(110,720)(111,719)(112,718)(113,713)(114,716)(115,715)(116,714)(117,709)(118,712)(119,711)(120,710)(121,705)(122,708)(123,707)(124,706)(125,701)(126,704)(127,703)(128,702)(129,697)(130,700)(131,699)(132,698)(133,693)(134,696)(135,695)(136,694)(137,689)(138,692)(139,691)(140,690)(141,685)(142,688)(143,687)(144,686)(145,681)(146,684)(147,683)(148,682)(149,677)(150,680)(151,679)(152,678)(153,673)(154,676)(155,675)(156,674)(157,669)(158,672)(159,671)(160,670)(161,665)(162,668)(163,667)(164,666)(165,497)(166,500)(167,499)(168,498)(169,493)(170,496)(171,495)(172,494)(173,653)(174,656)(175,655)(176,654)(177,649)(178,652)(179,651)(180,650)(181,645)(182,648)(183,647)(184,646)(185,641)(186,644)(187,643)(188,642)(189,637)(190,640)(191,639)(192,638)(193,633)(194,636)(195,635)(196,634)(197,629)(198,632)(199,631)(200,630)(201,625)(202,628)(203,627)(204,626)(205,621)(206,624)(207,623)(208,622)(209,617)(210,620)(211,619)(212,618)(213,613)(214,616)(215,615)(216,614)(217,609)(218,612)(219,611)(220,610)(221,605)(222,608)(223,607)(224,606)(225,601)(226,604)(227,603)(228,602)(229,597)(230,600)(231,599)(232,598)(233,593)(234,596)(235,595)(236,594)(237,589)(238,592)(239,591)(240,590)(241,585)(242,588)(243,587)(244,586)(245,581)(246,584)(247,583)(248,582)(249,577)(250,580)(251,579)(252,578)(253,573)(254,576)(255,575)(256,574)(257,569)(258,572)(259,571)(260,570)(261,565)(262,568)(263,567)(264,566)(265,561)(266,564)(267,563)(268,562)(269,557)(270,560)(271,559)(272,558)(273,553)(274,556)(275,555)(276,554)(277,549)(278,552)(279,551)(280,550)(281,545)(282,548)(283,547)(284,546)(285,541)(286,544)(287,543)(288,542)(289,537)(290,540)(291,539)(292,538)(293,533)(294,536)(295,535)(296,534)(297,529)(298,532)(299,531)(300,530)(301,525)(302,528)(303,527)(304,526)(305,521)(306,524)(307,523)(308,522)(309,517)(310,520)(311,519)(312,518)(313,513)(314,516)(315,515)(316,514)(317,509)(318,512)(319,511)(320,510)(321,505)(322,508)(323,507)(324,506)(325,501)(326,504)(327,503)(328,502)(329,825)(330,828)(331,827)(332,826)(333,821)(334,824)(335,823)(336,822)(337,981)(338,984)(339,983)(340,982)(341,977)(342,980)(343,979)(344,978)(345,973)(346,976)(347,975)(348,974)(349,969)(350,972)(351,971)(352,970)(353,965)(354,968)(355,967)(356,966)(357,961)(358,964)(359,963)(360,962)(361,957)(362,960)(363,959)(364,958)(365,953)(366,956)(367,955)(368,954)(369,949)(370,952)(371,951)(372,950)(373,945)(374,948)(375,947)(376,946)(377,941)(378,944)(379,943)(380,942)(381,937)(382,940)(383,939)(384,938)(385,933)(386,936)(387,935)(388,934)(389,929)(390,932)(391,931)(392,930)(393,925)(394,928)(395,927)(396,926)(397,921)(398,924)(399,923)(400,922)(401,917)(402,920)(403,919)(404,918)(405,913)(406,916)(407,915)(408,914)(409,909)(410,912)(411,911)(412,910)(413,905)(414,908)(415,907)(416,906)(417,901)(418,904)(419,903)(420,902)(421,897)(422,900)(423,899)(424,898)(425,893)(426,896)(427,895)(428,894)(429,889)(430,892)(431,891)(432,890)(433,885)(434,888)(435,887)(436,886)(437,881)(438,884)(439,883)(440,882)(441,877)(442,880)(443,879)(444,878)(445,873)(446,876)(447,875)(448,874)(449,869)(450,872)(451,871)(452,870)(453,865)(454,868)(455,867)(456,866)(457,861)(458,864)(459,863)(460,862)(461,857)(462,860)(463,859)(464,858)(465,853)(466,856)(467,855)(468,854)(469,849)(470,852)(471,851)(472,850)(473,845)
(474,848)(475,847)(476,846)(477,841)(478,844)(479,843)(480,842)(481,837)(482,840)(483,839)(484,838)(485,833)(486,836)(487,835)(488,834)(489,829)(490,832)(491,831)(492,830);
s2 := Sym(984)!(  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)(961,962)(963,964)(965,966)(967,968)(969,970)(971,972)(973,974)(975,976)(977,978)(979,980)(981,982)(983,984);
poly := sub<Sym(984)|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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1 >; 
 

Twisty Puzzle