Polytope of Type {28,16}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle