Polytope of Type {4,99}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle