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, 16)( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 37)( 30, 36)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 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, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 93)( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 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)(127,156)(128,155)(129,161)(130,160)(131,159)(132,158)(133,157)(134,163)(135,162)(136,168)(137,167)(138,166)(139,165)(140,164)(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)(183,212)(184,211)(185,217)(186,216)(187,215)(188,214)(189,213)(190,219)(191,218)(192,224)(193,223)(194,222)(195,221)(196,220)(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)(253,317)(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)(267,331)(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)(337,422)(338,421)(339,427)(340,426)(341,425)(342,424)(343,423)(344,429)(345,428)(346,434)(347,433)(348,432)(349,431)(350,430)(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)(365,394)(366,393)(367,399)(368,398)(369,397)(370,396)(371,395)(372,401)(373,400)(374,406)(375,405)(376,404)(377,403)(378,402)(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)(463,576)(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)(477,597)(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)(491,611)(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)(519,632)(520,631)(521,637)(522,636)(523,635)(524,634)(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)(532,640)(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)(547,667)(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)(687,842)(688,841)(689,847)(690,846)(691,845)(692,844)(693,843)(694,849)(695,848)(696,854)(697,853)(698,852)(699,851)(700,850)(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)(715,877)(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)(743,786)(744,785)(745,791)(746,790)(747,789)(748,788)(749,787)(750,793)(751,792)(752,798)(753,797)(754,796)(755,795)(756,794)(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)(771,821)(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)( 29,484)( 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);;
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, 
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, 
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, 16)( 17, 21)( 18, 20)( 22, 23)( 24, 28)( 25, 27)( 29, 37)( 30, 36)( 31, 42)( 32, 41)( 33, 40)( 34, 39)( 35, 38)( 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, 72)( 73, 77)( 74, 76)( 78, 79)( 80, 84)( 81, 83)( 85, 93)( 86, 92)( 87, 98)( 88, 97)( 89, 96)( 90, 95)( 91, 94)( 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)(127,156)(128,155)(129,161)(130,160)(131,159)(132,158)(133,157)(134,163)(135,162)(136,168)(137,167)(138,166)(139,165)(140,164)(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)(183,212)(184,211)(185,217)(186,216)(187,215)(188,214)(189,213)(190,219)(191,218)(192,224)(193,223)(194,222)(195,221)(196,220)(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)(253,317)(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)(267,331)(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)(337,422)(338,421)(339,427)(340,426)(341,425)(342,424)(343,423)(344,429)(345,428)(346,434)(347,433)(348,432)(349,431)(350,430)(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)(365,394)(366,393)(367,399)(368,398)(369,397)(370,396)(371,395)(372,401)(373,400)(374,406)(375,405)(376,404)(377,403)(378,402)(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)(463,576)(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)(477,597)(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)(491,611)(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)(519,632)(520,631)(521,637)(522,636)(523,635)(524,634)(525,633)(526,639)(527,638)(528,644)(529,643)(530,642)(531,641)(532,640)(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)(547,667)(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)(687,842)(688,841)(689,847)(690,846)(691,845)(692,844)(693,843)(694,849)(695,848)(696,854)(697,853)(698,852)(699,851)(700,850)(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)(715,877)(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)(743,786)(744,785)(745,791)(746,790)(747,789)(748,788)(749,787)(750,793)(751,792)(752,798)(753,797)(754,796)(755,795)(756,794)(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)(771,821)(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)( 29,484)( 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);
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, 
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, 
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