Polytope of Type {244,4}

Play with this polytope as a twisty puzzle

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