Polytope of Type {56,8}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle