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

Twisty Puzzle