Polytope of Type {8,51}

Play with this polytope as a twisty puzzle

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