Polytope of Type {51,8}

Play with this polytope as a twisty puzzle

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