Polytope of Type {248,4}

Play with this polytope as a twisty puzzle

s0 := (  1,497)(  2,527)(  3,526)(  4,525)(  5,524)(  6,523)(  7,522)(  8,521)(  9,520)( 10,519)( 11,518)( 12,517)( 13,516)( 14,515)( 15,514)( 16,513)( 17,512)( 18,511)( 19,510)( 20,509)
( 21,508)( 22,507)( 23,506)( 24,505)( 25,504)( 26,503)( 27,502)( 28,501)( 29,500)( 30,499)( 31,498)( 32,528)( 33,558)( 34,557)( 35,556)( 36,555)( 37,554)( 38,553)( 39,552)( 40,551)( 41,550)( 42,549)( 43,548)( 44,547)( 45,546)( 46,545)( 47,544)( 48,543)( 49,542)( 50,541)( 51,540)( 52,539)( 53,538)( 54,537)( 55,536)( 56,535)( 57,534)( 58,533)( 59,532)( 60,531)( 61,530)( 62,529)( 63,590)( 64,620)( 65,619)( 66,618)( 67,617)( 68,616)( 69,615)( 70,614)( 71,613)( 72,612)( 73,611)( 74,610)( 75,609)( 76,608)( 77,607)( 78,606)( 79,605)( 80,604)( 81,603)( 82,602)( 83,601)( 84,600)( 85,599)( 86,598)( 87,597)( 88,596)( 89,595)( 90,594)( 91,593)( 92,592)( 93,591)( 94,559)( 95,589)( 96,588)( 97,587)( 98,586)( 99,585)(100,584)(101,583)(102,582)(103,581)(104,580)(105,579)(106,578)(107,577)(108,576)(109,575)(110,574)(111,573)(112,572)(113,571)(114,570)(115,569)(116,568)(117,567)(118,566)(119,565)(120,564)(121,563)(122,562)(123,561)(124,560)(125,652)(126,682)(127,681)(128,680)(129,679)(130,678)(131,677)(132,676)(133,675)(134,674)(135,673)(136,672)(137,671)(138,670)(139,669)(140,668)(141,667)(142,666)(143,665)(144,664)(145,663)(146,662)(147,661)(148,660)(149,659)(150,658)(151,657)(152,656)(153,655)(154,654)(155,653)(156,621)(157,651)(158,650)(159,649)(160,648)(161,647)(162,646)(163,645)(164,644)(165,643)(166,642)(167,641)(168,640)(169,639)(170,638)(171,637)(172,636)(173,635)(174,634)(175,633)(176,632)(177,631)(178,630)(179,629)(180,628)(181,627)(182,626)(183,625)(184,624)(185,623)(186,622)(187,683)(188,713)(189,712)(190,711)(191,710)(192,709)(193,708)(194,707)(195,706)(196,705)(197,704)(198,703)(199,702)(200,701)(201,700)(202,699)(203,698)(204,697)(205,696)(206,695)(207,694)(208,693)(209,692)(210,691)(211,690)(212,689)(213,688)(214,687)(215,686)(216,685)(217,684)(218,714)(219,744)(220,743)(221,742)(222,741)(223,740)(224,739)(225,738)(226,737)(227,736)(228,735)(229,734)(230,733)(231,732)(232,731)(233,730)(234,729)(235,728)(236,727)(237,726)(238,725)(239,724)(240,723)(241,722)(242,721)(243,720)(244,719)(245,718)(246,717)(247,716)(248,715)(249,745)(250,775)(251,774)(252,773)(253,772)(254,771)(255,770)(256,769)(257,768)(258,767)(259,766)(260,765)(261,764)(262,763)(263,762)(264,761)(265,760)(266,759)(267,758)(268,757)(269,756)(270,755)(271,754)(272,753)(273,752)(274,751)(275,750)(276,749)(277,748)(278,747)(279,746)(280,776)(281,806)(282,805)(283,804)(284,803)(285,802)(286,801)(287,800)(288,799)(289,798)(290,797)(291,796)(292,795)(293,794)(294,793)(295,792)(296,791)(297,790)(298,789)(299,788)(300,787)(301,786)(302,785)(303,784)(304,783)(305,782)(306,781)(307,780)(308,779)(309,778)(310,777)(311,838)(312,868)(313,867)(314,866)(315,865)(316,864)(317,863)(318,862)(319,861)(320,860)(321,859)(322,858)(323,857)(324,856)(325,855)(326,854)(327,853)(328,852)(329,851)(330,850)(331,849)(332,848)(333,847)(334,846)(335,845)(336,844)(337,843)(338,842)(339,841)(340,840)(341,839)(342,807)(343,837)(344,836)(345,835)(346,834)(347,833)(348,832)(349,831)(350,830)(351,829)(352,828)(353,827)(354,826)(355,825)(356,824)(357,823)(358,822)(359,821)(360,820)(361,819)(362,818)(363,817)(364,816)(365,815)(366,814)(367,813)(368,812)(369,811)(370,810)(371,809)(372,808)(373,900)(374,930)(375,929)(376,928)(377,927)(378,926)(379,925)(380,924)(381,923)(382,922)(383,921)(384,920)(385,919)(386,918)(387,917)(388,916)(389,915)(390,914)(391,913)(392,912)(393,911)(394,910)(395,909)(396,908)(397,907)(398,906)(399,905)(400,904)(401,903)(402,902)(403,901)(404,869)(405,899)(406,898)(407,897)(408,896)(409,895)(410,894)(411,893)(412,892)(413,891)(414,890)(415,889)(416,888)(417,887)(418,886)(419,885)(420,884)(421,883)(422,882)(423,881)(424,880)(425,879)(426,878)(427,877)(428,876)(429,875)(430,874)(431,873)(432,872)(433,871)(434,870)(435,931)(436,961)(437,960)(438,959)(439,958)(440,957)(441,956)(442,955)(443,954)(444,953)(445,952)(446,951)(447,950)(448,949)(449,948)(450,947)(451,946)(452,945)(453,944)(454,943)(455,942)(456,941)(457,940)(458,939)(459,938)(460,937)(461,936)(462,935)(463,934)(464,933)(465,932)(466,962)(467,992)(468,991)(469,990)(470,989)(471,988)(472,987)(473,986)(474,985)
(475,984)(476,983)(477,982)(478,981)(479,980)(480,979)(481,978)(482,977)(483,976)(484,975)(485,974)(486,973)(487,972)(488,971)(489,970)(490,969)(491,968)(492,967)(493,966)(494,965)(495,964)(496,963);;
s1 := (  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)(  9, 25)( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 32, 33)( 34, 62)( 35, 61)( 36, 60)( 37, 59)
( 38, 58)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)( 65, 93)( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 94, 95)( 96,124)( 97,123)( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)(104,116)(105,115)(106,114)(107,113)(108,112)(109,111)(125,157)(126,156)(127,186)(128,185)(129,184)(130,183)(131,182)(132,181)(133,180)(134,179)(135,178)(136,177)(137,176)(138,175)(139,174)(140,173)(141,172)(142,171)(143,170)(144,169)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)(152,161)(153,160)(154,159)(155,158)(187,219)(188,218)(189,248)(190,247)(191,246)(192,245)(193,244)(194,243)(195,242)(196,241)(197,240)(198,239)(199,238)(200,237)(201,236)(202,235)(203,234)(204,233)(205,232)(206,231)(207,230)(208,229)(209,228)(210,227)(211,226)(212,225)(213,224)(214,223)(215,222)(216,221)(217,220)(249,312)(250,311)(251,341)(252,340)(253,339)(254,338)(255,337)(256,336)(257,335)(258,334)(259,333)(260,332)(261,331)(262,330)(263,329)(264,328)(265,327)(266,326)(267,325)(268,324)(269,323)(270,322)(271,321)(272,320)(273,319)(274,318)(275,317)(276,316)(277,315)(278,314)(279,313)(280,343)(281,342)(282,372)(283,371)(284,370)(285,369)(286,368)(287,367)(288,366)(289,365)(290,364)(291,363)(292,362)(293,361)(294,360)(295,359)(296,358)(297,357)(298,356)(299,355)(300,354)(301,353)(302,352)(303,351)(304,350)(305,349)(306,348)(307,347)(308,346)(309,345)(310,344)(373,467)(374,466)(375,496)(376,495)(377,494)(378,493)(379,492)(380,491)(381,490)(382,489)(383,488)(384,487)(385,486)(386,485)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,468)(404,436)(405,435)(406,465)(407,464)(408,463)(409,462)(410,461)(411,460)(412,459)(413,458)(414,457)(415,456)(416,455)(417,454)(418,453)(419,452)(420,451)(421,450)(422,449)(423,448)(424,447)(425,446)(426,445)(427,444)(428,443)(429,442)(430,441)(431,440)(432,439)(433,438)(434,437)(497,622)(498,621)(499,651)(500,650)(501,649)(502,648)(503,647)(504,646)(505,645)(506,644)(507,643)(508,642)(509,641)(510,640)(511,639)(512,638)(513,637)(514,636)(515,635)(516,634)(517,633)(518,632)(519,631)(520,630)(521,629)(522,628)(523,627)(524,626)(525,625)(526,624)(527,623)(528,653)(529,652)(530,682)(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)(538,674)(539,673)(540,672)(541,671)(542,670)(543,669)(544,668)(545,667)(546,666)(547,665)(548,664)(549,663)(550,662)(551,661)(552,660)(553,659)(554,658)(555,657)(556,656)(557,655)(558,654)(559,684)(560,683)(561,713)(562,712)(563,711)(564,710)(565,709)(566,708)(567,707)(568,706)(569,705)(570,704)(571,703)(572,702)(573,701)(574,700)(575,699)(576,698)(577,697)(578,696)(579,695)(580,694)(581,693)(582,692)(583,691)(584,690)(585,689)(586,688)(587,687)(588,686)(589,685)(590,715)(591,714)(592,744)(593,743)(594,742)(595,741)(596,740)(597,739)(598,738)(599,737)(600,736)(601,735)(602,734)(603,733)(604,732)(605,731)(606,730)(607,729)(608,728)(609,727)(610,726)(611,725)(612,724)(613,723)(614,722)(615,721)(616,720)(617,719)(618,718)(619,717)(620,716)(745,963)(746,962)(747,992)(748,991)(749,990)(750,989)(751,988)(752,987)(753,986)(754,985)(755,984)(756,983)(757,982)(758,981)(759,980)(760,979)(761,978)(762,977)(763,976)(764,975)(765,974)(766,973)(767,972)(768,971)(769,970)(770,969)(771,968)(772,967)(773,966)(774,965)(775,964)(776,932)(777,931)(778,961)(779,960)(780,959)(781,958)(782,957)(783,956)(784,955)(785,954)(786,953)(787,952)(788,951)(789,950)(790,949)(791,948)(792,947)(793,946)(794,945)(795,944)(796,943)(797,942)(798,941)(799,940)(800,939)(801,938)(802,937)(803,936)(804,935)(805,934)(806,933)(807,901)(808,900)(809,930)(810,929)(811,928)(812,927)(813,926)(814,925)(815,924)(816,923)(817,922)(818,921)(819,920)(820,919)(821,918)(822,917)(823,916)(824,915)(825,914)(826,913)(827,912)(828,911)(829,910)(830,909)(831,908)(832,907)(833,906)(834,905)(835,904)(836,903)(837,902)(838,870)(839,869)(840,899)(841,898)(842,897)(843,896)(844,895)(845,894)(846,893)(847,892)(848,891)
(849,890)(850,889)(851,888)(852,887)(853,886)(854,885)(855,884)(856,883)(857,882)(858,881)(859,880)(860,879)(861,878)(862,877)(863,876)(864,875)(865,874)(866,873)(867,872)(868,871);;
s2 := (  1,249)(  2,250)(  3,251)(  4,252)(  5,253)(  6,254)(  7,255)(  8,256)(  9,257)( 10,258)( 11,259)( 12,260)( 13,261)( 14,262)( 15,263)( 16,264)( 17,265)( 18,266)( 19,267)( 20,268)
( 21,269)( 22,270)( 23,271)( 24,272)( 25,273)( 26,274)( 27,275)( 28,276)( 29,277)( 30,278)( 31,279)( 32,280)( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)( 48,296)( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)( 57,305)( 58,306)( 59,307)( 60,308)( 61,309)( 62,310)( 63,311)( 64,312)( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)( 73,321)( 74,322)( 75,323)( 76,324)( 77,325)( 78,326)( 79,327)( 80,328)( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)( 96,344)( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)(105,353)(106,354)(107,355)(108,356)(109,357)(110,358)(111,359)(112,360)(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)(121,369)(122,370)(123,371)(124,372)(125,404)(126,405)(127,406)(128,407)(129,408)(130,409)(131,410)(132,411)(133,412)(134,413)(135,414)(136,415)(137,416)(138,417)(139,418)(140,419)(141,420)(142,421)(143,422)(144,423)(145,424)(146,425)(147,426)(148,427)(149,428)(150,429)(151,430)(152,431)(153,432)(154,433)(155,434)(156,373)(157,374)(158,375)(159,376)(160,377)(161,378)(162,379)(163,380)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)(170,387)(171,388)(172,389)(173,390)(174,391)(175,392)(176,393)(177,394)(178,395)(179,396)(180,397)(181,398)(182,399)(183,400)(184,401)(185,402)(186,403)(187,466)(188,467)(189,468)(190,469)(191,470)(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,478)(200,479)(201,480)(202,481)(203,482)(204,483)(205,484)(206,485)(207,486)(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)(217,496)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)(224,441)(225,442)(226,443)(227,444)(228,445)(229,446)(230,447)(231,448)(232,449)(233,450)(234,451)(235,452)(236,453)(237,454)(238,455)(239,456)(240,457)(241,458)(242,459)(243,460)(244,461)(245,462)(246,463)(247,464)(248,465)(497,745)(498,746)(499,747)(500,748)(501,749)(502,750)(503,751)(504,752)(505,753)(506,754)(507,755)(508,756)(509,757)(510,758)(511,759)(512,760)(513,761)(514,762)(515,763)(516,764)(517,765)(518,766)(519,767)(520,768)(521,769)(522,770)(523,771)(524,772)(525,773)(526,774)(527,775)(528,776)(529,777)(530,778)(531,779)(532,780)(533,781)(534,782)(535,783)(536,784)(537,785)(538,786)(539,787)(540,788)(541,789)(542,790)(543,791)(544,792)(545,793)(546,794)(547,795)(548,796)(549,797)(550,798)(551,799)(552,800)(553,801)(554,802)(555,803)(556,804)(557,805)(558,806)(559,807)(560,808)(561,809)(562,810)(563,811)(564,812)(565,813)(566,814)(567,815)(568,816)(569,817)(570,818)(571,819)(572,820)(573,821)(574,822)(575,823)(576,824)(577,825)(578,826)(579,827)(580,828)(581,829)(582,830)(583,831)(584,832)(585,833)(586,834)(587,835)(588,836)(589,837)(590,838)(591,839)(592,840)(593,841)(594,842)(595,843)(596,844)(597,845)(598,846)(599,847)(600,848)(601,849)(602,850)(603,851)(604,852)(605,853)(606,854)(607,855)(608,856)(609,857)(610,858)(611,859)(612,860)(613,861)(614,862)(615,863)(616,864)(617,865)(618,866)(619,867)(620,868)(621,900)(622,901)(623,902)(624,903)(625,904)(626,905)(627,906)(628,907)(629,908)(630,909)(631,910)(632,911)(633,912)(634,913)(635,914)(636,915)(637,916)(638,917)(639,918)(640,919)(641,920)(642,921)(643,922)(644,923)(645,924)(646,925)(647,926)(648,927)(649,928)(650,929)(651,930)(652,869)(653,870)(654,871)(655,872)(656,873)(657,874)(658,875)(659,876)(660,877)(661,878)(662,879)(663,880)(664,881)(665,882)(666,883)(667,884)(668,885)(669,886)(670,887)(671,888)(672,889)(673,890)(674,891)(675,892)(676,893)(677,894)(678,895)(679,896)(680,897)(681,898)(682,899)(683,962)(684,963)(685,964)(686,965)(687,966)(688,967)(689,968)(690,969)(691,970)(692,971)(693,972)(694,973)(695,974)(696,975)(697,976)(698,977)(699,978)(700,979)(701,980)(702,981)(703,982)(704,983)(705,984)(706,985)(707,986)(708,987)(709,988)(710,989)(711,990)(712,991)(713,992)(714,931)(715,932)(716,933)(717,934)(718,935)(719,936)(720,937)(721,938)(722,939)
(723,940)(724,941)(725,942)(726,943)(727,944)(728,945)(729,946)(730,947)(731,948)(732,949)(733,950)(734,951)(735,952)(736,953)(737,954)(738,955)(739,956)(740,957)(741,958)(742,959)(743,960)(744,961);;
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*s2*s1*s2*s1*s0*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*s2*s1*s0*s1*s0*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 ];;
poly := F / rels;;
 

s0 := Sym(992)!(  1,497)(  2,527)(  3,526)(  4,525)(  5,524)(  6,523)(  7,522)(  8,521)(  9,520)( 10,519)( 11,518)( 12,517)( 13,516)( 14,515)( 15,514)( 16,513)( 17,512)( 18,511)( 19,510)
( 20,509)( 21,508)( 22,507)( 23,506)( 24,505)( 25,504)( 26,503)( 27,502)( 28,501)( 29,500)( 30,499)( 31,498)( 32,528)( 33,558)( 34,557)( 35,556)( 36,555)( 37,554)( 38,553)( 39,552)( 40,551)( 41,550)( 42,549)( 43,548)( 44,547)( 45,546)( 46,545)( 47,544)( 48,543)( 49,542)( 50,541)( 51,540)( 52,539)( 53,538)( 54,537)( 55,536)( 56,535)( 57,534)( 58,533)( 59,532)( 60,531)( 61,530)( 62,529)( 63,590)( 64,620)( 65,619)( 66,618)( 67,617)( 68,616)( 69,615)( 70,614)( 71,613)( 72,612)( 73,611)( 74,610)( 75,609)( 76,608)( 77,607)( 78,606)( 79,605)( 80,604)( 81,603)( 82,602)( 83,601)( 84,600)( 85,599)( 86,598)( 87,597)( 88,596)( 89,595)( 90,594)( 91,593)( 92,592)( 93,591)( 94,559)( 95,589)( 96,588)( 97,587)( 98,586)( 99,585)(100,584)(101,583)(102,582)(103,581)(104,580)(105,579)(106,578)(107,577)(108,576)(109,575)(110,574)(111,573)(112,572)(113,571)(114,570)(115,569)(116,568)(117,567)(118,566)(119,565)(120,564)(121,563)(122,562)(123,561)(124,560)(125,652)(126,682)(127,681)(128,680)(129,679)(130,678)(131,677)(132,676)(133,675)(134,674)(135,673)(136,672)(137,671)(138,670)(139,669)(140,668)(141,667)(142,666)(143,665)(144,664)(145,663)(146,662)(147,661)(148,660)(149,659)(150,658)(151,657)(152,656)(153,655)(154,654)(155,653)(156,621)(157,651)(158,650)(159,649)(160,648)(161,647)(162,646)(163,645)(164,644)(165,643)(166,642)(167,641)(168,640)(169,639)(170,638)(171,637)(172,636)(173,635)(174,634)(175,633)(176,632)(177,631)(178,630)(179,629)(180,628)(181,627)(182,626)(183,625)(184,624)(185,623)(186,622)(187,683)(188,713)(189,712)(190,711)(191,710)(192,709)(193,708)(194,707)(195,706)(196,705)(197,704)(198,703)(199,702)(200,701)(201,700)(202,699)(203,698)(204,697)(205,696)(206,695)(207,694)(208,693)(209,692)(210,691)(211,690)(212,689)(213,688)(214,687)(215,686)(216,685)(217,684)(218,714)(219,744)(220,743)(221,742)(222,741)(223,740)(224,739)(225,738)(226,737)(227,736)(228,735)(229,734)(230,733)(231,732)(232,731)(233,730)(234,729)(235,728)(236,727)(237,726)(238,725)(239,724)(240,723)(241,722)(242,721)(243,720)(244,719)(245,718)(246,717)(247,716)(248,715)(249,745)(250,775)(251,774)(252,773)(253,772)(254,771)(255,770)(256,769)(257,768)(258,767)(259,766)(260,765)(261,764)(262,763)(263,762)(264,761)(265,760)(266,759)(267,758)(268,757)(269,756)(270,755)(271,754)(272,753)(273,752)(274,751)(275,750)(276,749)(277,748)(278,747)(279,746)(280,776)(281,806)(282,805)(283,804)(284,803)(285,802)(286,801)(287,800)(288,799)(289,798)(290,797)(291,796)(292,795)(293,794)(294,793)(295,792)(296,791)(297,790)(298,789)(299,788)(300,787)(301,786)(302,785)(303,784)(304,783)(305,782)(306,781)(307,780)(308,779)(309,778)(310,777)(311,838)(312,868)(313,867)(314,866)(315,865)(316,864)(317,863)(318,862)(319,861)(320,860)(321,859)(322,858)(323,857)(324,856)(325,855)(326,854)(327,853)(328,852)(329,851)(330,850)(331,849)(332,848)(333,847)(334,846)(335,845)(336,844)(337,843)(338,842)(339,841)(340,840)(341,839)(342,807)(343,837)(344,836)(345,835)(346,834)(347,833)(348,832)(349,831)(350,830)(351,829)(352,828)(353,827)(354,826)(355,825)(356,824)(357,823)(358,822)(359,821)(360,820)(361,819)(362,818)(363,817)(364,816)(365,815)(366,814)(367,813)(368,812)(369,811)(370,810)(371,809)(372,808)(373,900)(374,930)(375,929)(376,928)(377,927)(378,926)(379,925)(380,924)(381,923)(382,922)(383,921)(384,920)(385,919)(386,918)(387,917)(388,916)(389,915)(390,914)(391,913)(392,912)(393,911)(394,910)(395,909)(396,908)(397,907)(398,906)(399,905)(400,904)(401,903)(402,902)(403,901)(404,869)(405,899)(406,898)(407,897)(408,896)(409,895)(410,894)(411,893)(412,892)(413,891)(414,890)(415,889)(416,888)(417,887)(418,886)(419,885)(420,884)(421,883)(422,882)(423,881)(424,880)(425,879)(426,878)(427,877)(428,876)(429,875)(430,874)(431,873)(432,872)(433,871)(434,870)(435,931)(436,961)(437,960)(438,959)(439,958)(440,957)(441,956)(442,955)(443,954)(444,953)(445,952)(446,951)(447,950)(448,949)(449,948)(450,947)(451,946)(452,945)(453,944)(454,943)(455,942)(456,941)(457,940)(458,939)(459,938)(460,937)(461,936)(462,935)(463,934)(464,933)(465,932)(466,962)(467,992)(468,991)(469,990)(470,989)(471,988)(472,987)(473,986)
(474,985)(475,984)(476,983)(477,982)(478,981)(479,980)(480,979)(481,978)(482,977)(483,976)(484,975)(485,974)(486,973)(487,972)(488,971)(489,970)(490,969)(491,968)(492,967)(493,966)(494,965)(495,964)(496,963);
s1 := Sym(992)!(  1,  2)(  3, 31)(  4, 30)(  5, 29)(  6, 28)(  7, 27)(  8, 26)(  9, 25)( 10, 24)( 11, 23)( 12, 22)( 13, 21)( 14, 20)( 15, 19)( 16, 18)( 32, 33)( 34, 62)( 35, 61)( 36, 60)
( 37, 59)( 38, 58)( 39, 57)( 40, 56)( 41, 55)( 42, 54)( 43, 53)( 44, 52)( 45, 51)( 46, 50)( 47, 49)( 63, 64)( 65, 93)( 66, 92)( 67, 91)( 68, 90)( 69, 89)( 70, 88)( 71, 87)( 72, 86)( 73, 85)( 74, 84)( 75, 83)( 76, 82)( 77, 81)( 78, 80)( 94, 95)( 96,124)( 97,123)( 98,122)( 99,121)(100,120)(101,119)(102,118)(103,117)(104,116)(105,115)(106,114)(107,113)(108,112)(109,111)(125,157)(126,156)(127,186)(128,185)(129,184)(130,183)(131,182)(132,181)(133,180)(134,179)(135,178)(136,177)(137,176)(138,175)(139,174)(140,173)(141,172)(142,171)(143,170)(144,169)(145,168)(146,167)(147,166)(148,165)(149,164)(150,163)(151,162)(152,161)(153,160)(154,159)(155,158)(187,219)(188,218)(189,248)(190,247)(191,246)(192,245)(193,244)(194,243)(195,242)(196,241)(197,240)(198,239)(199,238)(200,237)(201,236)(202,235)(203,234)(204,233)(205,232)(206,231)(207,230)(208,229)(209,228)(210,227)(211,226)(212,225)(213,224)(214,223)(215,222)(216,221)(217,220)(249,312)(250,311)(251,341)(252,340)(253,339)(254,338)(255,337)(256,336)(257,335)(258,334)(259,333)(260,332)(261,331)(262,330)(263,329)(264,328)(265,327)(266,326)(267,325)(268,324)(269,323)(270,322)(271,321)(272,320)(273,319)(274,318)(275,317)(276,316)(277,315)(278,314)(279,313)(280,343)(281,342)(282,372)(283,371)(284,370)(285,369)(286,368)(287,367)(288,366)(289,365)(290,364)(291,363)(292,362)(293,361)(294,360)(295,359)(296,358)(297,357)(298,356)(299,355)(300,354)(301,353)(302,352)(303,351)(304,350)(305,349)(306,348)(307,347)(308,346)(309,345)(310,344)(373,467)(374,466)(375,496)(376,495)(377,494)(378,493)(379,492)(380,491)(381,490)(382,489)(383,488)(384,487)(385,486)(386,485)(387,484)(388,483)(389,482)(390,481)(391,480)(392,479)(393,478)(394,477)(395,476)(396,475)(397,474)(398,473)(399,472)(400,471)(401,470)(402,469)(403,468)(404,436)(405,435)(406,465)(407,464)(408,463)(409,462)(410,461)(411,460)(412,459)(413,458)(414,457)(415,456)(416,455)(417,454)(418,453)(419,452)(420,451)(421,450)(422,449)(423,448)(424,447)(425,446)(426,445)(427,444)(428,443)(429,442)(430,441)(431,440)(432,439)(433,438)(434,437)(497,622)(498,621)(499,651)(500,650)(501,649)(502,648)(503,647)(504,646)(505,645)(506,644)(507,643)(508,642)(509,641)(510,640)(511,639)(512,638)(513,637)(514,636)(515,635)(516,634)(517,633)(518,632)(519,631)(520,630)(521,629)(522,628)(523,627)(524,626)(525,625)(526,624)(527,623)(528,653)(529,652)(530,682)(531,681)(532,680)(533,679)(534,678)(535,677)(536,676)(537,675)(538,674)(539,673)(540,672)(541,671)(542,670)(543,669)(544,668)(545,667)(546,666)(547,665)(548,664)(549,663)(550,662)(551,661)(552,660)(553,659)(554,658)(555,657)(556,656)(557,655)(558,654)(559,684)(560,683)(561,713)(562,712)(563,711)(564,710)(565,709)(566,708)(567,707)(568,706)(569,705)(570,704)(571,703)(572,702)(573,701)(574,700)(575,699)(576,698)(577,697)(578,696)(579,695)(580,694)(581,693)(582,692)(583,691)(584,690)(585,689)(586,688)(587,687)(588,686)(589,685)(590,715)(591,714)(592,744)(593,743)(594,742)(595,741)(596,740)(597,739)(598,738)(599,737)(600,736)(601,735)(602,734)(603,733)(604,732)(605,731)(606,730)(607,729)(608,728)(609,727)(610,726)(611,725)(612,724)(613,723)(614,722)(615,721)(616,720)(617,719)(618,718)(619,717)(620,716)(745,963)(746,962)(747,992)(748,991)(749,990)(750,989)(751,988)(752,987)(753,986)(754,985)(755,984)(756,983)(757,982)(758,981)(759,980)(760,979)(761,978)(762,977)(763,976)(764,975)(765,974)(766,973)(767,972)(768,971)(769,970)(770,969)(771,968)(772,967)(773,966)(774,965)(775,964)(776,932)(777,931)(778,961)(779,960)(780,959)(781,958)(782,957)(783,956)(784,955)(785,954)(786,953)(787,952)(788,951)(789,950)(790,949)(791,948)(792,947)(793,946)(794,945)(795,944)(796,943)(797,942)(798,941)(799,940)(800,939)(801,938)(802,937)(803,936)(804,935)(805,934)(806,933)(807,901)(808,900)(809,930)(810,929)(811,928)(812,927)(813,926)(814,925)(815,924)(816,923)(817,922)(818,921)(819,920)(820,919)(821,918)(822,917)(823,916)(824,915)(825,914)(826,913)(827,912)(828,911)(829,910)(830,909)(831,908)(832,907)(833,906)(834,905)(835,904)(836,903)(837,902)(838,870)(839,869)(840,899)(841,898)(842,897)(843,896)(844,895)(845,894)(846,893)(847,892)
(848,891)(849,890)(850,889)(851,888)(852,887)(853,886)(854,885)(855,884)(856,883)(857,882)(858,881)(859,880)(860,879)(861,878)(862,877)(863,876)(864,875)(865,874)(866,873)(867,872)(868,871);
s2 := Sym(992)!(  1,249)(  2,250)(  3,251)(  4,252)(  5,253)(  6,254)(  7,255)(  8,256)(  9,257)( 10,258)( 11,259)( 12,260)( 13,261)( 14,262)( 15,263)( 16,264)( 17,265)( 18,266)( 19,267)
( 20,268)( 21,269)( 22,270)( 23,271)( 24,272)( 25,273)( 26,274)( 27,275)( 28,276)( 29,277)( 30,278)( 31,279)( 32,280)( 33,281)( 34,282)( 35,283)( 36,284)( 37,285)( 38,286)( 39,287)( 40,288)( 41,289)( 42,290)( 43,291)( 44,292)( 45,293)( 46,294)( 47,295)( 48,296)( 49,297)( 50,298)( 51,299)( 52,300)( 53,301)( 54,302)( 55,303)( 56,304)( 57,305)( 58,306)( 59,307)( 60,308)( 61,309)( 62,310)( 63,311)( 64,312)( 65,313)( 66,314)( 67,315)( 68,316)( 69,317)( 70,318)( 71,319)( 72,320)( 73,321)( 74,322)( 75,323)( 76,324)( 77,325)( 78,326)( 79,327)( 80,328)( 81,329)( 82,330)( 83,331)( 84,332)( 85,333)( 86,334)( 87,335)( 88,336)( 89,337)( 90,338)( 91,339)( 92,340)( 93,341)( 94,342)( 95,343)( 96,344)( 97,345)( 98,346)( 99,347)(100,348)(101,349)(102,350)(103,351)(104,352)(105,353)(106,354)(107,355)(108,356)(109,357)(110,358)(111,359)(112,360)(113,361)(114,362)(115,363)(116,364)(117,365)(118,366)(119,367)(120,368)(121,369)(122,370)(123,371)(124,372)(125,404)(126,405)(127,406)(128,407)(129,408)(130,409)(131,410)(132,411)(133,412)(134,413)(135,414)(136,415)(137,416)(138,417)(139,418)(140,419)(141,420)(142,421)(143,422)(144,423)(145,424)(146,425)(147,426)(148,427)(149,428)(150,429)(151,430)(152,431)(153,432)(154,433)(155,434)(156,373)(157,374)(158,375)(159,376)(160,377)(161,378)(162,379)(163,380)(164,381)(165,382)(166,383)(167,384)(168,385)(169,386)(170,387)(171,388)(172,389)(173,390)(174,391)(175,392)(176,393)(177,394)(178,395)(179,396)(180,397)(181,398)(182,399)(183,400)(184,401)(185,402)(186,403)(187,466)(188,467)(189,468)(190,469)(191,470)(192,471)(193,472)(194,473)(195,474)(196,475)(197,476)(198,477)(199,478)(200,479)(201,480)(202,481)(203,482)(204,483)(205,484)(206,485)(207,486)(208,487)(209,488)(210,489)(211,490)(212,491)(213,492)(214,493)(215,494)(216,495)(217,496)(218,435)(219,436)(220,437)(221,438)(222,439)(223,440)(224,441)(225,442)(226,443)(227,444)(228,445)(229,446)(230,447)(231,448)(232,449)(233,450)(234,451)(235,452)(236,453)(237,454)(238,455)(239,456)(240,457)(241,458)(242,459)(243,460)(244,461)(245,462)(246,463)(247,464)(248,465)(497,745)(498,746)(499,747)(500,748)(501,749)(502,750)(503,751)(504,752)(505,753)(506,754)(507,755)(508,756)(509,757)(510,758)(511,759)(512,760)(513,761)(514,762)(515,763)(516,764)(517,765)(518,766)(519,767)(520,768)(521,769)(522,770)(523,771)(524,772)(525,773)(526,774)(527,775)(528,776)(529,777)(530,778)(531,779)(532,780)(533,781)(534,782)(535,783)(536,784)(537,785)(538,786)(539,787)(540,788)(541,789)(542,790)(543,791)(544,792)(545,793)(546,794)(547,795)(548,796)(549,797)(550,798)(551,799)(552,800)(553,801)(554,802)(555,803)(556,804)(557,805)(558,806)(559,807)(560,808)(561,809)(562,810)(563,811)(564,812)(565,813)(566,814)(567,815)(568,816)(569,817)(570,818)(571,819)(572,820)(573,821)(574,822)(575,823)(576,824)(577,825)(578,826)(579,827)(580,828)(581,829)(582,830)(583,831)(584,832)(585,833)(586,834)(587,835)(588,836)(589,837)(590,838)(591,839)(592,840)(593,841)(594,842)(595,843)(596,844)(597,845)(598,846)(599,847)(600,848)(601,849)(602,850)(603,851)(604,852)(605,853)(606,854)(607,855)(608,856)(609,857)(610,858)(611,859)(612,860)(613,861)(614,862)(615,863)(616,864)(617,865)(618,866)(619,867)(620,868)(621,900)(622,901)(623,902)(624,903)(625,904)(626,905)(627,906)(628,907)(629,908)(630,909)(631,910)(632,911)(633,912)(634,913)(635,914)(636,915)(637,916)(638,917)(639,918)(640,919)(641,920)(642,921)(643,922)(644,923)(645,924)(646,925)(647,926)(648,927)(649,928)(650,929)(651,930)(652,869)(653,870)(654,871)(655,872)(656,873)(657,874)(658,875)(659,876)(660,877)(661,878)(662,879)(663,880)(664,881)(665,882)(666,883)(667,884)(668,885)(669,886)(670,887)(671,888)(672,889)(673,890)(674,891)(675,892)(676,893)(677,894)(678,895)(679,896)(680,897)(681,898)(682,899)(683,962)(684,963)(685,964)(686,965)(687,966)(688,967)(689,968)(690,969)(691,970)(692,971)(693,972)(694,973)(695,974)(696,975)(697,976)(698,977)(699,978)(700,979)(701,980)(702,981)(703,982)(704,983)(705,984)(706,985)(707,986)(708,987)(709,988)(710,989)(711,990)(712,991)(713,992)(714,931)(715,932)(716,933)(717,934)(718,935)(719,936)(720,937)(721,938)
(722,939)(723,940)(724,941)(725,942)(726,943)(727,944)(728,945)(729,946)(730,947)(731,948)(732,949)(733,950)(734,951)(735,952)(736,953)(737,954)(738,955)(739,956)(740,957)(741,958)(742,959)(743,960)(744,961);
poly := sub<Sym(992)|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*s2*s1*s2*s1*s0*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*s2*s1*s0*s1*s0*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 >; 
 

Twisty Puzzle