Polytope of Type {62,16}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle