Polytope of Type {52,8}

Play with this polytope as a twisty puzzle

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