Polytope of Type {198,4}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle