Polytope of Type {104,4}

Play with this polytope as a twisty puzzle

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