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)( 53,469)( 54,470)( 55,471)( 56,472)( 57,473)( 58,474)( 59,475)( 60,476)( 61,477)( 62,478)( 63,479)( 64,480)( 65,481)( 66,482)( 67,483)( 68,484)( 69,485)( 70,486)( 71,487)( 72,488)( 73,489)( 74,490)( 75,491)( 76,492)( 77,493)( 78,494)( 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)(157,599)(158,600)(159,601)(160,602)(161,603)(162,604)(163,605)(164,606)(165,607)(166,608)(167,609)(168,610)(169,611)(170,612)(171,613)(172,614)(173,615)(174,616)(175,617)(176,618)(177,619)(178,620)(179,621)(180,622)(181,623)(182,624)(183,573)(184,574)(185,575)(186,576)(187,577)(188,578)(189,579)(190,580)(191,581)(192,582)(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)(200,590)(201,591)(202,592)(203,593)(204,594)(205,595)(206,596)(207,597)(208,598)(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)(261,677)(262,678)(263,679)(264,680)(265,681)(266,682)(267,683)(268,684)(269,685)(270,686)(271,687)(272,688)(273,689)(274,690)(275,691)(276,692)(277,693)(278,694)(279,695)(280,696)(281,697)(282,698)(283,699)(284,700)(285,701)(286,702)(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)(365,807)(366,808)(367,809)(368,810)(369,811)(370,812)(371,813)(372,814)(373,815)(374,816)(375,817)(376,818)(377,819)(378,820)(379,821)(380,822)(381,823)(382,824)(383,825)(384,826)(385,827)(386,828)(387,829)(388,830)(389,831)(390,832)(391,781)(392,782)(393,783)(394,784)(395,785)(396,786)(397,787)(398,788)(399,789)(400,790)(401,791)(402,792)(403,793)(404,794)(405,795)(406,796)(407,797)(408,798)(409,799)(410,800)(411,801)(412,802)(413,803)(414,804)(415,805)(416,806);;
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)(625,781)(626,793)(627,792)(628,791)(629,790)(630,789)(631,788)(632,787)(633,786)(634,785)(635,784)(636,783)(637,782)(638,794)(639,806)(640,805)(641,804)(642,803)(643,802)(644,801)(645,800)(646,799)(647,798)(648,797)(649,796)(650,795)(651,820)(652,832)(653,831)(654,830)(655,829)(656,828)(657,827)(658,826)(659,825)(660,824)(661,823)(662,822)(663,821)(664,807)(665,819)(666,818)(667,817)(668,816)(669,815)(670,814)(671,813)(672,812)(673,811)(674,810)(675,809)(676,808)(677,729)(678,741)(679,740)(680,739)(681,738)(682,737)(683,736)(684,735)(685,734)(686,733)(687,732)(688,731)(689,730)(690,742)(691,754)(692,753)(693,752)(694,751)(695,750)(696,749)(697,748)(698,747)(699,746)(700,745)(701,744)(702,743)(703,768)(704,780)(705,779)(706,778)(707,777)(708,776)(709,775)(710,774)(711,773)(712,772)(713,771)(714,770)(715,769)(716,755)(717,767)(718,766)(719,765)(720,764)(721,763)(722,762)(723,761)(724,760)(725,759)(726,758)(727,757)(728,756);;
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)(105,314)(106,313)(107,325)(108,324)(109,323)(110,322)(111,321)(112,320)(113,319)(114,318)(115,317)(116,316)(117,315)(118,327)(119,326)(120,338)(121,337)(122,336)(123,335)(124,334)(125,333)(126,332)(127,331)(128,330)(129,329)(130,328)(131,340)(132,339)(133,351)(134,350)(135,349)(136,348)(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)(144,353)(145,352)(146,364)(147,363)(148,362)(149,361)(150,360)(151,359)(152,358)(153,357)(154,356)(155,355)(156,354)(157,366)(158,365)(159,377)(160,376)(161,375)(162,374)(163,373)(164,372)(165,371)(166,370)(167,369)(168,368)(169,367)(170,379)(171,378)(172,390)(173,389)(174,388)(175,387)(176,386)(177,385)(178,384)(179,383)(180,382)(181,381)(182,380)(183,392)(184,391)(185,403)(186,402)(187,401)(188,400)(189,399)(190,398)(191,397)(192,396)(193,395)(194,394)(195,393)(196,405)(197,404)(198,416)(199,415)(200,414)(201,413)(202,412)(203,411)(204,410)(205,409)(206,408)(207,407)(208,406)(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)(521,730)(522,729)(523,741)(524,740)(525,739)(526,738)(527,737)(528,736)(529,735)(530,734)(531,733)(532,732)(533,731)(534,743)(535,742)(536,754)(537,753)(538,752)(539,751)(540,750)(541,749)(542,748)(543,747)(544,746)(545,745)(546,744)(547,756)(548,755)(549,767)(550,766)(551,765)(552,764)(553,763)(554,762)(555,761)(556,760)(557,759)(558,758)(559,757)(560,769)(561,768)(562,780)(563,779)(564,778)(565,777)(566,776)(567,775)(568,774)(569,773)(570,772)(571,771)(572,770)(573,782)(574,781)(575,793)(576,792)(577,791)(578,790)(579,789)(580,788)(581,787)(582,786)(583,785)(584,784)(585,783)(586,795)(587,794)(588,806)(589,805)(590,804)(591,803)(592,802)(593,801)(594,800)(595,799)(596,798)(597,797)(598,796)(599,808)(600,807)(601,819)(602,818)(603,817)(604,816)(605,815)(606,814)(607,813)(608,812)(609,811)(610,810)(611,809)(612,821)(613,820)(614,832)(615,831)(616,830)(617,829)(618,828)(619,827)(620,826)(621,825)(622,824)(623,823)(624,822);;
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*s0*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*s0*s1*s0*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)( 53,469)( 54,470)( 55,471)( 56,472)( 57,473)( 58,474)( 59,475)( 60,476)( 61,477)( 62,478)( 63,479)( 64,480)( 65,481)( 66,482)( 67,483)( 68,484)( 69,485)( 70,486)( 71,487)( 72,488)( 73,489)( 74,490)( 75,491)( 76,492)( 77,493)( 78,494)( 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)(157,599)(158,600)(159,601)(160,602)(161,603)(162,604)(163,605)(164,606)(165,607)(166,608)(167,609)(168,610)(169,611)(170,612)(171,613)(172,614)(173,615)(174,616)(175,617)(176,618)(177,619)(178,620)(179,621)(180,622)(181,623)(182,624)(183,573)(184,574)(185,575)(186,576)(187,577)(188,578)(189,579)(190,580)(191,581)(192,582)(193,583)(194,584)(195,585)(196,586)(197,587)(198,588)(199,589)(200,590)(201,591)(202,592)(203,593)(204,594)(205,595)(206,596)(207,597)(208,598)(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)(261,677)(262,678)(263,679)(264,680)(265,681)(266,682)(267,683)(268,684)(269,685)(270,686)(271,687)(272,688)(273,689)(274,690)(275,691)(276,692)(277,693)(278,694)(279,695)(280,696)(281,697)(282,698)(283,699)(284,700)(285,701)(286,702)(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)(365,807)(366,808)(367,809)(368,810)(369,811)(370,812)(371,813)(372,814)(373,815)(374,816)(375,817)(376,818)(377,819)(378,820)(379,821)(380,822)(381,823)(382,824)(383,825)(384,826)(385,827)(386,828)(387,829)(388,830)(389,831)(390,832)(391,781)(392,782)(393,783)(394,784)(395,785)(396,786)(397,787)(398,788)(399,789)(400,790)(401,791)(402,792)(403,793)(404,794)(405,795)(406,796)(407,797)(408,798)(409,799)(410,800)(411,801)(412,802)(413,803)(414,804)(415,805)(416,806);
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)(625,781)(626,793)(627,792)(628,791)(629,790)(630,789)(631,788)(632,787)(633,786)(634,785)(635,784)(636,783)(637,782)(638,794)(639,806)(640,805)(641,804)(642,803)(643,802)(644,801)(645,800)(646,799)(647,798)(648,797)(649,796)(650,795)(651,820)(652,832)(653,831)(654,830)(655,829)(656,828)(657,827)(658,826)(659,825)(660,824)(661,823)(662,822)(663,821)(664,807)(665,819)(666,818)(667,817)(668,816)(669,815)(670,814)(671,813)(672,812)(673,811)(674,810)(675,809)(676,808)(677,729)(678,741)(679,740)(680,739)(681,738)(682,737)(683,736)(684,735)(685,734)(686,733)(687,732)(688,731)(689,730)(690,742)(691,754)(692,753)(693,752)(694,751)(695,750)(696,749)(697,748)(698,747)(699,746)(700,745)(701,744)(702,743)(703,768)(704,780)(705,779)(706,778)(707,777)(708,776)(709,775)(710,774)(711,773)(712,772)(713,771)(714,770)(715,769)(716,755)(717,767)(718,766)(719,765)(720,764)(721,763)(722,762)(723,761)(724,760)(725,759)(726,758)(727,757)(728,756);
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)(105,314)(106,313)(107,325)(108,324)(109,323)(110,322)(111,321)(112,320)(113,319)(114,318)(115,317)(116,316)(117,315)(118,327)(119,326)(120,338)(121,337)(122,336)(123,335)(124,334)(125,333)(126,332)(127,331)(128,330)(129,329)(130,328)(131,340)(132,339)(133,351)(134,350)(135,349)(136,348)(137,347)(138,346)(139,345)(140,344)(141,343)(142,342)(143,341)(144,353)(145,352)(146,364)(147,363)(148,362)(149,361)(150,360)(151,359)(152,358)(153,357)(154,356)(155,355)(156,354)(157,366)(158,365)(159,377)(160,376)(161,375)(162,374)(163,373)(164,372)(165,371)(166,370)(167,369)(168,368)(169,367)(170,379)(171,378)(172,390)(173,389)(174,388)(175,387)(176,386)(177,385)(178,384)(179,383)(180,382)(181,381)(182,380)(183,392)(184,391)(185,403)(186,402)(187,401)(188,400)(189,399)(190,398)(191,397)(192,396)(193,395)(194,394)(195,393)(196,405)(197,404)(198,416)(199,415)(200,414)(201,413)(202,412)(203,411)(204,410)(205,409)(206,408)(207,407)(208,406)(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)(521,730)(522,729)(523,741)(524,740)(525,739)(526,738)(527,737)(528,736)(529,735)(530,734)(531,733)(532,732)(533,731)(534,743)(535,742)(536,754)(537,753)(538,752)(539,751)(540,750)(541,749)(542,748)(543,747)(544,746)(545,745)(546,744)(547,756)(548,755)(549,767)(550,766)(551,765)(552,764)(553,763)(554,762)(555,761)(556,760)(557,759)(558,758)(559,757)(560,769)(561,768)(562,780)(563,779)(564,778)(565,777)(566,776)(567,775)(568,774)(569,773)(570,772)(571,771)(572,770)(573,782)(574,781)(575,793)(576,792)(577,791)(578,790)(579,789)(580,788)(581,787)(582,786)(583,785)(584,784)(585,783)(586,795)(587,794)(588,806)(589,805)(590,804)(591,803)(592,802)(593,801)(594,800)(595,799)(596,798)(597,797)(598,796)(599,808)(600,807)(601,819)(602,818)(603,817)(604,816)(605,815)(606,814)(607,813)(608,812)(609,811)(610,810)(611,809)(612,821)(613,820)(614,832)(615,831)(616,830)(617,829)(618,828)(619,827)(620,826)(621,825)(622,824)(623,823)(624,822);
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*s0*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*s0*s1*s0*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