Polytope of Type {16,56}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle