Polytope of Type {4,225}

Play with this polytope as a twisty puzzle

s0 := (  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480)(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)(494,496)(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)(510,512)(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)(526,528)(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)(542,544)(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)(558,560)(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)(574,576)(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)(590,592)(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)(606,608)(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)(622,624)(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)(638,640)(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)(654,656)(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)(670,672)(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)(686,688)(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)(702,704)(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)(718,720)(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)(734,736)(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)(750,752)(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)(766,768)(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)(782,784)(785,787)(786,788)(789,791)(790,792)(793,795)(794,796)(797,799)(798,800)(801,803)(802,804)(805,807)(806,808)(809,811)(810,812)(813,815)(814,816)(817,819)(818,820)(821,823)(822,824)(825,827)(826,828)(829,831)(830,832)(833,835)(834,836)(837,839)(838,840)(841,843)(842,844)(845,847)(846,848)(849,851)(850,852)(853,855)(854,856)(857,859)(858,860)(861,863)(862,864)(865,867)(866,868)(869,871)(870,872)(873,875)(874,876)(877,879)(878,880)(881,883)(882,884)(885,887)(886,888)(889,891)(890,892)(893,895)(894,896)(897,899)(898,900);;
s1 := (  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 61,257)( 62,258)( 63,260)( 64,259)( 65,253)( 66,254)( 67,256)( 68,255)( 69,249)( 70,250)( 71,252)( 72,251)( 73,245)( 74,246)( 75,248)( 76,247)( 77,241)( 78,242)( 79,244)( 80,243)( 81,297)( 82,298)( 83,300)( 84,299)( 85,293)( 86,294)( 87,296)( 88,295)( 89,289)( 90,290)( 91,292)( 92,291)( 93,285)( 94,286)( 95,288)( 96,287)( 97,281)( 98,282)( 99,284)(100,283)(101,277)(102,278)(103,280)(104,279)(105,273)(106,274)(107,276)(108,275)(109,269)(110,270)(111,272)(112,271)(113,265)(114,266)(115,268)(116,267)(117,261)(118,262)(119,264)(120,263)(121,197)(122,198)(123,200)(124,199)(125,193)(126,194)(127,196)(128,195)(129,189)(130,190)(131,192)(132,191)(133,185)(134,186)(135,188)(136,187)(137,181)(138,182)(139,184)(140,183)(141,237)(142,238)(143,240)(144,239)(145,233)(146,234)(147,236)(148,235)(149,229)(150,230)(151,232)(152,231)(153,225)(154,226)(155,228)(156,227)(157,221)(158,222)(159,224)(160,223)(161,217)(162,218)(163,220)(164,219)(165,213)(166,214)(167,216)(168,215)(169,209)(170,210)(171,212)(172,211)(173,205)(174,206)(175,208)(176,207)(177,201)(178,202)(179,204)(180,203)(301,641)(302,642)(303,644)(304,643)(305,657)(306,658)(307,660)(308,659)(309,653)(310,654)(311,656)(312,655)(313,649)(314,650)(315,652)(316,651)(317,645)(318,646)(319,648)(320,647)(321,621)(322,622)(323,624)(324,623)(325,637)(326,638)(327,640)(328,639)(329,633)(330,634)(331,636)(332,635)(333,629)(334,630)(335,632)(336,631)(337,625)(338,626)(339,628)(340,627)(341,601)(342,602)(343,604)(344,603)(345,617)(346,618)(347,620)(348,619)(349,613)(350,614)(351,616)(352,615)(353,609)(354,610)(355,612)(356,611)(357,605)(358,606)(359,608)(360,607)(361,897)(362,898)(363,900)(364,899)(365,893)(366,894)(367,896)(368,895)(369,889)(370,890)(371,892)(372,891)(373,885)(374,886)(375,888)(376,887)(377,881)(378,882)(379,884)(380,883)(381,877)(382,878)(383,880)(384,879)(385,873)(386,874)(387,876)(388,875)(389,869)(390,870)(391,872)(392,871)(393,865)(394,866)(395,868)(396,867)(397,861)(398,862)(399,864)(400,863)(401,857)(402,858)(403,860)(404,859)(405,853)(406,854)(407,856)(408,855)(409,849)(410,850)(411,852)(412,851)(413,845)(414,846)(415,848)(416,847)(417,841)(418,842)(419,844)(420,843)(421,837)(422,838)(423,840)(424,839)(425,833)(426,834)(427,836)(428,835)(429,829)(430,830)(431,832)(432,831)(433,825)(434,826)(435,828)(436,827)(437,821)(438,822)(439,824)(440,823)(441,817)(442,818)(443,820)(444,819)(445,813)(446,814)(447,816)(448,815)(449,809)(450,810)(451,812)(452,811)(453,805)(454,806)(455,808)(456,807)(457,801)(458,802)(459,804)(460,803)(461,797)(462,798)(463,800)(464,799)(465,793)(466,794)(467,796)(468,795)(469,789)(470,790)(471,792)(472,791)(473,785)(474,786)(475,788)(476,787)(477,781)(478,782)(479,784)(480,783)(481,777)(482,778)(483,780)(484,779)(485,773)(486,774)(487,776)(488,775)(489,769)(490,770)(491,772)(492,771)(493,765)(494,766)(495,768)(496,767)(497,761)(498,762)(499,764)(500,763)(501,757)(502,758)(503,760)(504,759)(505,753)(506,754)(507,756)(508,755)(509,749)(510,750)(511,752)(512,751)(513,745)(514,746)(515,748)(516,747)(517,741)(518,742)(519,744)(520,743)(521,737)(522,738)(523,740)(524,739)(525,733)(526,734)(527,736)(528,735)(529,729)(530,730)(531,732)(532,731)(533,725)(534,726)(535,728)(536,727)(537,721)(538,722)(539,724)(540,723)(541,717)(542,718)(543,720)(544,719)(545,713)(546,714)(547,716)(548,715)(549,709)(550,710)(551,712)(552,711)(553,705)(554,706)(555,708)(556,707)(557,701)(558,702)(559,704)(560,703)(561,697)(562,698)(563,700)(564,699)(565,693)(566,694)(567,696)(568,695)(569,689)(570,690)(571,692)(572,691)(573,685)(574,686)(575,688)(576,687)(577,681)(578,682)(579,684)(580,683)(581,677)(582,678)(583,680)(584,679)(585,673)(586,674)(587,676)(588,675)(589,669)(590,670)(591,672)(592,671)(593,665)(594,666)(595,668)(596,667)(597,661)(598,662)(599,664)(600,663);;
s2 := (  1,361)(  2,364)(  3,363)(  4,362)(  5,377)(  6,380)(  7,379)(  8,378)(  9,373)( 10,376)( 11,375)( 12,374)( 13,369)( 14,372)( 15,371)( 16,370)( 17,365)( 18,368)( 19,367)( 20,366)( 21,401)( 22,404)( 23,403)( 24,402)( 25,417)( 26,420)( 27,419)( 28,418)( 29,413)( 30,416)( 31,415)( 32,414)( 33,409)( 34,412)( 35,411)( 36,410)( 37,405)( 38,408)( 39,407)( 40,406)( 41,381)( 42,384)( 43,383)( 44,382)( 45,397)( 46,400)( 47,399)( 48,398)( 49,393)( 50,396)( 51,395)( 52,394)( 53,389)( 54,392)( 55,391)( 56,390)( 57,385)( 58,388)( 59,387)( 60,386)( 61,301)( 62,304)( 63,303)( 64,302)( 65,317)( 66,320)( 67,319)( 68,318)( 69,313)( 70,316)( 71,315)( 72,314)( 73,309)( 74,312)( 75,311)( 76,310)( 77,305)( 78,308)( 79,307)( 80,306)( 81,341)( 82,344)( 83,343)( 84,342)( 85,357)( 86,360)( 87,359)( 88,358)( 89,353)( 90,356)( 91,355)( 92,354)( 93,349)( 94,352)( 95,351)( 96,350)( 97,345)( 98,348)( 99,347)(100,346)(101,321)(102,324)(103,323)(104,322)(105,337)(106,340)(107,339)(108,338)(109,333)(110,336)(111,335)(112,334)(113,329)(114,332)(115,331)(116,330)(117,325)(118,328)(119,327)(120,326)(121,557)(122,560)(123,559)(124,558)(125,553)(126,556)(127,555)(128,554)(129,549)(130,552)(131,551)(132,550)(133,545)(134,548)(135,547)(136,546)(137,541)(138,544)(139,543)(140,542)(141,597)(142,600)(143,599)(144,598)(145,593)(146,596)(147,595)(148,594)(149,589)(150,592)(151,591)(152,590)(153,585)(154,588)(155,587)(156,586)(157,581)(158,584)(159,583)(160,582)(161,577)(162,580)(163,579)(164,578)(165,573)(166,576)(167,575)(168,574)(169,569)(170,572)(171,571)(172,570)(173,565)(174,568)(175,567)(176,566)(177,561)(178,564)(179,563)(180,562)(181,497)(182,500)(183,499)(184,498)(185,493)(186,496)(187,495)(188,494)(189,489)(190,492)(191,491)(192,490)(193,485)(194,488)(195,487)(196,486)(197,481)(198,484)(199,483)(200,482)(201,537)(202,540)(203,539)(204,538)(205,533)(206,536)(207,535)(208,534)(209,529)(210,532)(211,531)(212,530)(213,525)(214,528)(215,527)(216,526)(217,521)(218,524)(219,523)(220,522)(221,517)(222,520)(223,519)(224,518)(225,513)(226,516)(227,515)(228,514)(229,509)(230,512)(231,511)(232,510)(233,505)(234,508)(235,507)(236,506)(237,501)(238,504)(239,503)(240,502)(241,437)(242,440)(243,439)(244,438)(245,433)(246,436)(247,435)(248,434)(249,429)(250,432)(251,431)(252,430)(253,425)(254,428)(255,427)(256,426)(257,421)(258,424)(259,423)(260,422)(261,477)(262,480)(263,479)(264,478)(265,473)(266,476)(267,475)(268,474)(269,469)(270,472)(271,471)(272,470)(273,465)(274,468)(275,467)(276,466)(277,461)(278,464)(279,463)(280,462)(281,457)(282,460)(283,459)(284,458)(285,453)(286,456)(287,455)(288,454)(289,449)(290,452)(291,451)(292,450)(293,445)(294,448)(295,447)(296,446)(297,441)(298,444)(299,443)(300,442)(601,701)(602,704)(603,703)(604,702)(605,717)(606,720)(607,719)(608,718)(609,713)(610,716)(611,715)(612,714)(613,709)(614,712)(615,711)(616,710)(617,705)(618,708)(619,707)(620,706)(621,681)(622,684)(623,683)(624,682)(625,697)(626,700)(627,699)(628,698)(629,693)(630,696)(631,695)(632,694)(633,689)(634,692)(635,691)(636,690)(637,685)(638,688)(639,687)(640,686)(641,661)(642,664)(643,663)(644,662)(645,677)(646,680)(647,679)(648,678)(649,673)(650,676)(651,675)(652,674)(653,669)(654,672)(655,671)(656,670)(657,665)(658,668)(659,667)(660,666)(721,897)(722,900)(723,899)(724,898)(725,893)(726,896)(727,895)(728,894)(729,889)(730,892)(731,891)(732,890)(733,885)(734,888)(735,887)(736,886)(737,881)(738,884)(739,883)(740,882)(741,877)(742,880)(743,879)(744,878)(745,873)(746,876)(747,875)(748,874)(749,869)(750,872)(751,871)(752,870)(753,865)(754,868)(755,867)(756,866)(757,861)(758,864)(759,863)(760,862)(761,857)(762,860)(763,859)(764,858)(765,853)(766,856)(767,855)(768,854)(769,849)(770,852)(771,851)(772,850)(773,845)(774,848)(775,847)(776,846)(777,841)(778,844)(779,843)(780,842)(781,837)(782,840)(783,839)(784,838)(785,833)(786,836)(787,835)(788,834)(789,829)(790,832)(791,831)(792,830)(793,825)(794,828)(795,827)(796,826)(797,821)(798,824)(799,823)(800,822)(801,817)(802,820)(803,819)(804,818)(805,813)(806,816)(807,815)(808,814)(810,812);;
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*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*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*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*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*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*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*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*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*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*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*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*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*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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 ];;
poly := F / rels;;
 

s0 := Sym(900)!(  1,  3)(  2,  4)(  5,  7)(  6,  8)(  9, 11)( 10, 12)( 13, 15)( 14, 16)( 17, 19)( 18, 20)( 21, 23)( 22, 24)( 25, 27)( 26, 28)( 29, 31)( 30, 32)( 33, 35)( 34, 36)( 37, 39)( 38, 40)( 41, 43)( 42, 44)( 45, 47)( 46, 48)( 49, 51)( 50, 52)( 53, 55)( 54, 56)( 57, 59)( 58, 60)( 61, 63)( 62, 64)( 65, 67)( 66, 68)( 69, 71)( 70, 72)( 73, 75)( 74, 76)( 77, 79)( 78, 80)( 81, 83)( 82, 84)( 85, 87)( 86, 88)( 89, 91)( 90, 92)( 93, 95)( 94, 96)( 97, 99)( 98,100)(101,103)(102,104)(105,107)(106,108)(109,111)(110,112)(113,115)(114,116)(117,119)(118,120)(121,123)(122,124)(125,127)(126,128)(129,131)(130,132)(133,135)(134,136)(137,139)(138,140)(141,143)(142,144)(145,147)(146,148)(149,151)(150,152)(153,155)(154,156)(157,159)(158,160)(161,163)(162,164)(165,167)(166,168)(169,171)(170,172)(173,175)(174,176)(177,179)(178,180)(181,183)(182,184)(185,187)(186,188)(189,191)(190,192)(193,195)(194,196)(197,199)(198,200)(201,203)(202,204)(205,207)(206,208)(209,211)(210,212)(213,215)(214,216)(217,219)(218,220)(221,223)(222,224)(225,227)(226,228)(229,231)(230,232)(233,235)(234,236)(237,239)(238,240)(241,243)(242,244)(245,247)(246,248)(249,251)(250,252)(253,255)(254,256)(257,259)(258,260)(261,263)(262,264)(265,267)(266,268)(269,271)(270,272)(273,275)(274,276)(277,279)(278,280)(281,283)(282,284)(285,287)(286,288)(289,291)(290,292)(293,295)(294,296)(297,299)(298,300)(301,303)(302,304)(305,307)(306,308)(309,311)(310,312)(313,315)(314,316)(317,319)(318,320)(321,323)(322,324)(325,327)(326,328)(329,331)(330,332)(333,335)(334,336)(337,339)(338,340)(341,343)(342,344)(345,347)(346,348)(349,351)(350,352)(353,355)(354,356)(357,359)(358,360)(361,363)(362,364)(365,367)(366,368)(369,371)(370,372)(373,375)(374,376)(377,379)(378,380)(381,383)(382,384)(385,387)(386,388)(389,391)(390,392)(393,395)(394,396)(397,399)(398,400)(401,403)(402,404)(405,407)(406,408)(409,411)(410,412)(413,415)(414,416)(417,419)(418,420)(421,423)(422,424)(425,427)(426,428)(429,431)(430,432)(433,435)(434,436)(437,439)(438,440)(441,443)(442,444)(445,447)(446,448)(449,451)(450,452)(453,455)(454,456)(457,459)(458,460)(461,463)(462,464)(465,467)(466,468)(469,471)(470,472)(473,475)(474,476)(477,479)(478,480)(481,483)(482,484)(485,487)(486,488)(489,491)(490,492)(493,495)(494,496)(497,499)(498,500)(501,503)(502,504)(505,507)(506,508)(509,511)(510,512)(513,515)(514,516)(517,519)(518,520)(521,523)(522,524)(525,527)(526,528)(529,531)(530,532)(533,535)(534,536)(537,539)(538,540)(541,543)(542,544)(545,547)(546,548)(549,551)(550,552)(553,555)(554,556)(557,559)(558,560)(561,563)(562,564)(565,567)(566,568)(569,571)(570,572)(573,575)(574,576)(577,579)(578,580)(581,583)(582,584)(585,587)(586,588)(589,591)(590,592)(593,595)(594,596)(597,599)(598,600)(601,603)(602,604)(605,607)(606,608)(609,611)(610,612)(613,615)(614,616)(617,619)(618,620)(621,623)(622,624)(625,627)(626,628)(629,631)(630,632)(633,635)(634,636)(637,639)(638,640)(641,643)(642,644)(645,647)(646,648)(649,651)(650,652)(653,655)(654,656)(657,659)(658,660)(661,663)(662,664)(665,667)(666,668)(669,671)(670,672)(673,675)(674,676)(677,679)(678,680)(681,683)(682,684)(685,687)(686,688)(689,691)(690,692)(693,695)(694,696)(697,699)(698,700)(701,703)(702,704)(705,707)(706,708)(709,711)(710,712)(713,715)(714,716)(717,719)(718,720)(721,723)(722,724)(725,727)(726,728)(729,731)(730,732)(733,735)(734,736)(737,739)(738,740)(741,743)(742,744)(745,747)(746,748)(749,751)(750,752)(753,755)(754,756)(757,759)(758,760)(761,763)(762,764)(765,767)(766,768)(769,771)(770,772)(773,775)(774,776)(777,779)(778,780)(781,783)(782,784)(785,787)(786,788)(789,791)(790,792)(793,795)(794,796)(797,799)(798,800)(801,803)(802,804)(805,807)(806,808)(809,811)(810,812)(813,815)(814,816)(817,819)(818,820)(821,823)(822,824)(825,827)(826,828)(829,831)(830,832)(833,835)(834,836)(837,839)(838,840)(841,843)(842,844)(845,847)(846,848)(849,851)(850,852)(853,855)(854,856)(857,859)(858,860)(861,863)(862,864)(865,867)(866,868)(869,871)(870,872)(873,875)(874,876)(877,879)(878,880)(881,883)(882,884)(885,887)(886,888)(889,891)(890,892)(893,895)(894,896)(897,899)(898,900);
s1 := Sym(900)!(  3,  4)(  5, 17)(  6, 18)(  7, 20)(  8, 19)(  9, 13)( 10, 14)( 11, 16)( 12, 15)( 21, 41)( 22, 42)( 23, 44)( 24, 43)( 25, 57)( 26, 58)( 27, 60)( 28, 59)( 29, 53)( 30, 54)( 31, 56)( 32, 55)( 33, 49)( 34, 50)( 35, 52)( 36, 51)( 37, 45)( 38, 46)( 39, 48)( 40, 47)( 61,257)( 62,258)( 63,260)( 64,259)( 65,253)( 66,254)( 67,256)( 68,255)( 69,249)( 70,250)( 71,252)( 72,251)( 73,245)( 74,246)( 75,248)( 76,247)( 77,241)( 78,242)( 79,244)( 80,243)( 81,297)( 82,298)( 83,300)( 84,299)( 85,293)( 86,294)( 87,296)( 88,295)( 89,289)( 90,290)( 91,292)( 92,291)( 93,285)( 94,286)( 95,288)( 96,287)( 97,281)( 98,282)( 99,284)(100,283)(101,277)(102,278)(103,280)(104,279)(105,273)(106,274)(107,276)(108,275)(109,269)(110,270)(111,272)(112,271)(113,265)(114,266)(115,268)(116,267)(117,261)(118,262)(119,264)(120,263)(121,197)(122,198)(123,200)(124,199)(125,193)(126,194)(127,196)(128,195)(129,189)(130,190)(131,192)(132,191)(133,185)(134,186)(135,188)(136,187)(137,181)(138,182)(139,184)(140,183)(141,237)(142,238)(143,240)(144,239)(145,233)(146,234)(147,236)(148,235)(149,229)(150,230)(151,232)(152,231)(153,225)(154,226)(155,228)(156,227)(157,221)(158,222)(159,224)(160,223)(161,217)(162,218)(163,220)(164,219)(165,213)(166,214)(167,216)(168,215)(169,209)(170,210)(171,212)(172,211)(173,205)(174,206)(175,208)(176,207)(177,201)(178,202)(179,204)(180,203)(301,641)(302,642)(303,644)(304,643)(305,657)(306,658)(307,660)(308,659)(309,653)(310,654)(311,656)(312,655)(313,649)(314,650)(315,652)(316,651)(317,645)(318,646)(319,648)(320,647)(321,621)(322,622)(323,624)(324,623)(325,637)(326,638)(327,640)(328,639)(329,633)(330,634)(331,636)(332,635)(333,629)(334,630)(335,632)(336,631)(337,625)(338,626)(339,628)(340,627)(341,601)(342,602)(343,604)(344,603)(345,617)(346,618)(347,620)(348,619)(349,613)(350,614)(351,616)(352,615)(353,609)(354,610)(355,612)(356,611)(357,605)(358,606)(359,608)(360,607)(361,897)(362,898)(363,900)(364,899)(365,893)(366,894)(367,896)(368,895)(369,889)(370,890)(371,892)(372,891)(373,885)(374,886)(375,888)(376,887)(377,881)(378,882)(379,884)(380,883)(381,877)(382,878)(383,880)(384,879)(385,873)(386,874)(387,876)(388,875)(389,869)(390,870)(391,872)(392,871)(393,865)(394,866)(395,868)(396,867)(397,861)(398,862)(399,864)(400,863)(401,857)(402,858)(403,860)(404,859)(405,853)(406,854)(407,856)(408,855)(409,849)(410,850)(411,852)(412,851)(413,845)(414,846)(415,848)(416,847)(417,841)(418,842)(419,844)(420,843)(421,837)(422,838)(423,840)(424,839)(425,833)(426,834)(427,836)(428,835)(429,829)(430,830)(431,832)(432,831)(433,825)(434,826)(435,828)(436,827)(437,821)(438,822)(439,824)(440,823)(441,817)(442,818)(443,820)(444,819)(445,813)(446,814)(447,816)(448,815)(449,809)(450,810)(451,812)(452,811)(453,805)(454,806)(455,808)(456,807)(457,801)(458,802)(459,804)(460,803)(461,797)(462,798)(463,800)(464,799)(465,793)(466,794)(467,796)(468,795)(469,789)(470,790)(471,792)(472,791)(473,785)(474,786)(475,788)(476,787)(477,781)(478,782)(479,784)(480,783)(481,777)(482,778)(483,780)(484,779)(485,773)(486,774)(487,776)(488,775)(489,769)(490,770)(491,772)(492,771)(493,765)(494,766)(495,768)(496,767)(497,761)(498,762)(499,764)(500,763)(501,757)(502,758)(503,760)(504,759)(505,753)(506,754)(507,756)(508,755)(509,749)(510,750)(511,752)(512,751)(513,745)(514,746)(515,748)(516,747)(517,741)(518,742)(519,744)(520,743)(521,737)(522,738)(523,740)(524,739)(525,733)(526,734)(527,736)(528,735)(529,729)(530,730)(531,732)(532,731)(533,725)(534,726)(535,728)(536,727)(537,721)(538,722)(539,724)(540,723)(541,717)(542,718)(543,720)(544,719)(545,713)(546,714)(547,716)(548,715)(549,709)(550,710)(551,712)(552,711)(553,705)(554,706)(555,708)(556,707)(557,701)(558,702)(559,704)(560,703)(561,697)(562,698)(563,700)(564,699)(565,693)(566,694)(567,696)(568,695)(569,689)(570,690)(571,692)(572,691)(573,685)(574,686)(575,688)(576,687)(577,681)(578,682)(579,684)(580,683)(581,677)(582,678)(583,680)(584,679)(585,673)(586,674)(587,676)(588,675)(589,669)(590,670)(591,672)(592,671)(593,665)(594,666)(595,668)(596,667)(597,661)(598,662)(599,664)(600,663);
s2 := Sym(900)!(  1,361)(  2,364)(  3,363)(  4,362)(  5,377)(  6,380)(  7,379)(  8,378)(  9,373)( 10,376)( 11,375)( 12,374)( 13,369)( 14,372)( 15,371)( 16,370)( 17,365)( 18,368)( 19,367)( 20,366)( 21,401)( 22,404)( 23,403)( 24,402)( 25,417)( 26,420)( 27,419)( 28,418)( 29,413)( 30,416)( 31,415)( 32,414)( 33,409)( 34,412)( 35,411)( 36,410)( 37,405)( 38,408)( 39,407)( 40,406)( 41,381)( 42,384)( 43,383)( 44,382)( 45,397)( 46,400)( 47,399)( 48,398)( 49,393)( 50,396)( 51,395)( 52,394)( 53,389)( 54,392)( 55,391)( 56,390)( 57,385)( 58,388)( 59,387)( 60,386)( 61,301)( 62,304)( 63,303)( 64,302)( 65,317)( 66,320)( 67,319)( 68,318)( 69,313)( 70,316)( 71,315)( 72,314)( 73,309)( 74,312)( 75,311)( 76,310)( 77,305)( 78,308)( 79,307)( 80,306)( 81,341)( 82,344)( 83,343)( 84,342)( 85,357)( 86,360)( 87,359)( 88,358)( 89,353)( 90,356)( 91,355)( 92,354)( 93,349)( 94,352)( 95,351)( 96,350)( 97,345)( 98,348)( 99,347)(100,346)(101,321)(102,324)(103,323)(104,322)(105,337)(106,340)(107,339)(108,338)(109,333)(110,336)(111,335)(112,334)(113,329)(114,332)(115,331)(116,330)(117,325)(118,328)(119,327)(120,326)(121,557)(122,560)(123,559)(124,558)(125,553)(126,556)(127,555)(128,554)(129,549)(130,552)(131,551)(132,550)(133,545)(134,548)(135,547)(136,546)(137,541)(138,544)(139,543)(140,542)(141,597)(142,600)(143,599)(144,598)(145,593)(146,596)(147,595)(148,594)(149,589)(150,592)(151,591)(152,590)(153,585)(154,588)(155,587)(156,586)(157,581)(158,584)(159,583)(160,582)(161,577)(162,580)(163,579)(164,578)(165,573)(166,576)(167,575)(168,574)(169,569)(170,572)(171,571)(172,570)(173,565)(174,568)(175,567)(176,566)(177,561)(178,564)(179,563)(180,562)(181,497)(182,500)(183,499)(184,498)(185,493)(186,496)(187,495)(188,494)(189,489)(190,492)(191,491)(192,490)(193,485)(194,488)(195,487)(196,486)(197,481)(198,484)(199,483)(200,482)(201,537)(202,540)(203,539)(204,538)(205,533)(206,536)(207,535)(208,534)(209,529)(210,532)(211,531)(212,530)(213,525)(214,528)(215,527)(216,526)(217,521)(218,524)(219,523)(220,522)(221,517)(222,520)(223,519)(224,518)(225,513)(226,516)(227,515)(228,514)(229,509)(230,512)(231,511)(232,510)(233,505)(234,508)(235,507)(236,506)(237,501)(238,504)(239,503)(240,502)(241,437)(242,440)(243,439)(244,438)(245,433)(246,436)(247,435)(248,434)(249,429)(250,432)(251,431)(252,430)(253,425)(254,428)(255,427)(256,426)(257,421)(258,424)(259,423)(260,422)(261,477)(262,480)(263,479)(264,478)(265,473)(266,476)(267,475)(268,474)(269,469)(270,472)(271,471)(272,470)(273,465)(274,468)(275,467)(276,466)(277,461)(278,464)(279,463)(280,462)(281,457)(282,460)(283,459)(284,458)(285,453)(286,456)(287,455)(288,454)(289,449)(290,452)(291,451)(292,450)(293,445)(294,448)(295,447)(296,446)(297,441)(298,444)(299,443)(300,442)(601,701)(602,704)(603,703)(604,702)(605,717)(606,720)(607,719)(608,718)(609,713)(610,716)(611,715)(612,714)(613,709)(614,712)(615,711)(616,710)(617,705)(618,708)(619,707)(620,706)(621,681)(622,684)(623,683)(624,682)(625,697)(626,700)(627,699)(628,698)(629,693)(630,696)(631,695)(632,694)(633,689)(634,692)(635,691)(636,690)(637,685)(638,688)(639,687)(640,686)(641,661)(642,664)(643,663)(644,662)(645,677)(646,680)(647,679)(648,678)(649,673)(650,676)(651,675)(652,674)(653,669)(654,672)(655,671)(656,670)(657,665)(658,668)(659,667)(660,666)(721,897)(722,900)(723,899)(724,898)(725,893)(726,896)(727,895)(728,894)(729,889)(730,892)(731,891)(732,890)(733,885)(734,888)(735,887)(736,886)(737,881)(738,884)(739,883)(740,882)(741,877)(742,880)(743,879)(744,878)(745,873)(746,876)(747,875)(748,874)(749,869)(750,872)(751,871)(752,870)(753,865)(754,868)(755,867)(756,866)(757,861)(758,864)(759,863)(760,862)(761,857)(762,860)(763,859)(764,858)(765,853)(766,856)(767,855)(768,854)(769,849)(770,852)(771,851)(772,850)(773,845)(774,848)(775,847)(776,846)(777,841)(778,844)(779,843)(780,842)(781,837)(782,840)(783,839)(784,838)(785,833)(786,836)(787,835)(788,834)(789,829)(790,832)(791,831)(792,830)(793,825)(794,828)(795,827)(796,826)(797,821)(798,824)(799,823)(800,822)(801,817)(802,820)(803,819)(804,818)(805,813)(806,816)(807,815)(808,814)(810,812);
poly := sub<Sym(900)|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*s0*s1, 
s0*s1*s2*s1*s0*s1*s2*s0*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*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*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*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*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*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*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*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*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*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*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*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*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*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2 >; 
 

Twisty Puzzle