Polytope of Type {16,52}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle