Polytope of Type {8,104}

Play with this polytope as a twisty puzzle

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

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

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s0*s1*s0*s1*s2*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*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*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

Twisty Puzzle