Polytope of Type {210,4}

Play with this polytope as a twisty puzzle

s0 := (  3,  4)(  5, 25)(  6, 26)(  7, 28)(  8, 27)(  9, 21)( 10, 22)( 11, 24)( 12, 23)( 13, 17)( 14, 18)( 15, 20)( 16, 19)( 29,113)( 30,114)( 31,116)( 32,115)( 33,137)( 34,138)( 35,140)( 36,139)( 37,133)( 38,134)( 39,136)( 40,135)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)( 47,128)( 48,127)( 49,121)( 50,122)( 51,124)( 52,123)( 53,117)( 54,118)( 55,120)( 56,119)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61,109)( 62,110)( 63,112)( 64,111)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)( 71,104)( 72,103)( 73, 97)( 74, 98)( 75,100)( 76, 99)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)(141,281)(142,282)(143,284)(144,283)(145,305)(146,306)(147,308)(148,307)(149,301)(150,302)(151,304)(152,303)(153,297)(154,298)(155,300)(156,299)(157,293)(158,294)(159,296)(160,295)(161,289)(162,290)(163,292)(164,291)(165,285)(166,286)(167,288)(168,287)(169,393)(170,394)(171,396)(172,395)(173,417)(174,418)(175,420)(176,419)(177,413)(178,414)(179,416)(180,415)(181,409)(182,410)(183,412)(184,411)(185,405)(186,406)(187,408)(188,407)(189,401)(190,402)(191,404)(192,403)(193,397)(194,398)(195,400)(196,399)(197,365)(198,366)(199,368)(200,367)(201,389)(202,390)(203,392)(204,391)(205,385)(206,386)(207,388)(208,387)(209,381)(210,382)(211,384)(212,383)(213,377)(214,378)(215,380)(216,379)(217,373)(218,374)(219,376)(220,375)(221,369)(222,370)(223,372)(224,371)(225,337)(226,338)(227,340)(228,339)(229,361)(230,362)(231,364)(232,363)(233,357)(234,358)(235,360)(236,359)(237,353)(238,354)(239,356)(240,355)(241,349)(242,350)(243,352)(244,351)(245,345)(246,346)(247,348)(248,347)(249,341)(250,342)(251,344)(252,343)(253,309)(254,310)(255,312)(256,311)(257,333)(258,334)(259,336)(260,335)(261,329)(262,330)(263,332)(264,331)(265,325)(266,326)(267,328)(268,327)(269,321)(270,322)(271,324)(272,323)(273,317)(274,318)(275,320)(276,319)(277,313)(278,314)(279,316)(280,315)(423,424)(425,445)(426,446)(427,448)(428,447)(429,441)(430,442)(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(449,533)(450,534)(451,536)(452,535)(453,557)(454,558)(455,560)(456,559)(457,553)(458,554)(459,556)(460,555)(461,549)(462,550)(463,552)(464,551)(465,545)(466,546)(467,548)(468,547)(469,541)(470,542)(471,544)(472,543)(473,537)(474,538)(475,540)(476,539)(477,505)(478,506)(479,508)(480,507)(481,529)(482,530)(483,532)(484,531)(485,525)(486,526)(487,528)(488,527)(489,521)(490,522)(491,524)(492,523)(493,517)(494,518)(495,520)(496,519)(497,513)(498,514)(499,516)(500,515)(501,509)(502,510)(503,512)(504,511)(561,701)(562,702)(563,704)(564,703)(565,725)(566,726)(567,728)(568,727)(569,721)(570,722)(571,724)(572,723)(573,717)(574,718)(575,720)(576,719)(577,713)(578,714)(579,716)(580,715)(581,709)(582,710)(583,712)(584,711)(585,705)(586,706)(587,708)(588,707)(589,813)(590,814)(591,816)(592,815)(593,837)(594,838)(595,840)(596,839)(597,833)(598,834)(599,836)(600,835)(601,829)(602,830)(603,832)(604,831)(605,825)(606,826)(607,828)(608,827)(609,821)(610,822)(611,824)(612,823)(613,817)(614,818)(615,820)(616,819)(617,785)(618,786)(619,788)(620,787)(621,809)(622,810)(623,812)(624,811)(625,805)(626,806)(627,808)(628,807)(629,801)(630,802)(631,804)(632,803)(633,797)(634,798)(635,800)(636,799)(637,793)(638,794)(639,796)(640,795)(641,789)(642,790)(643,792)(644,791)(645,757)(646,758)(647,760)(648,759)(649,781)(650,782)(651,784)(652,783)(653,777)(654,778)(655,780)(656,779)(657,773)(658,774)(659,776)(660,775)(661,769)(662,770)(663,772)(664,771)(665,765)(666,766)(667,768)(668,767)(669,761)(670,762)(671,764)(672,763)(673,729)(674,730)(675,732)(676,731)(677,753)(678,754)(679,756)(680,755)(681,749)(682,750)(683,752)(684,751)(685,745)(686,746)(687,748)(688,747)(689,741)(690,742)(691,744)(692,743)(693,737)(694,738)(695,740)(696,739)(697,733)(698,734)(699,736)(700,735);;
s1 := (  1,593)(  2,596)(  3,595)(  4,594)(  5,589)(  6,592)(  7,591)(  8,590)(  9,613)( 10,616)( 11,615)( 12,614)( 13,609)( 14,612)( 15,611)( 16,610)( 17,605)( 18,608)( 19,607)( 20,606)( 21,601)( 22,604)( 23,603)( 24,602)( 25,597)( 26,600)( 27,599)( 28,598)( 29,565)( 30,568)( 31,567)( 32,566)( 33,561)( 34,564)( 35,563)( 36,562)( 37,585)( 38,588)( 39,587)( 40,586)( 41,581)( 42,584)( 43,583)( 44,582)( 45,577)( 46,580)( 47,579)( 48,578)( 49,573)( 50,576)( 51,575)( 52,574)( 53,569)( 54,572)( 55,571)( 56,570)( 57,677)( 58,680)( 59,679)( 60,678)( 61,673)( 62,676)( 63,675)( 64,674)( 65,697)( 66,700)( 67,699)( 68,698)( 69,693)( 70,696)( 71,695)( 72,694)( 73,689)( 74,692)( 75,691)( 76,690)( 77,685)( 78,688)( 79,687)( 80,686)( 81,681)( 82,684)( 83,683)( 84,682)( 85,649)( 86,652)( 87,651)( 88,650)( 89,645)( 90,648)( 91,647)( 92,646)( 93,669)( 94,672)( 95,671)( 96,670)( 97,665)( 98,668)( 99,667)(100,666)(101,661)(102,664)(103,663)(104,662)(105,657)(106,660)(107,659)(108,658)(109,653)(110,656)(111,655)(112,654)(113,621)(114,624)(115,623)(116,622)(117,617)(118,620)(119,619)(120,618)(121,641)(122,644)(123,643)(124,642)(125,637)(126,640)(127,639)(128,638)(129,633)(130,636)(131,635)(132,634)(133,629)(134,632)(135,631)(136,630)(137,625)(138,628)(139,627)(140,626)(141,453)(142,456)(143,455)(144,454)(145,449)(146,452)(147,451)(148,450)(149,473)(150,476)(151,475)(152,474)(153,469)(154,472)(155,471)(156,470)(157,465)(158,468)(159,467)(160,466)(161,461)(162,464)(163,463)(164,462)(165,457)(166,460)(167,459)(168,458)(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)(176,422)(177,445)(178,448)(179,447)(180,446)(181,441)(182,444)(183,443)(184,442)(185,437)(186,440)(187,439)(188,438)(189,433)(190,436)(191,435)(192,434)(193,429)(194,432)(195,431)(196,430)(197,537)(198,540)(199,539)(200,538)(201,533)(202,536)(203,535)(204,534)(205,557)(206,560)(207,559)(208,558)(209,553)(210,556)(211,555)(212,554)(213,549)(214,552)(215,551)(216,550)(217,545)(218,548)(219,547)(220,546)(221,541)(222,544)(223,543)(224,542)(225,509)(226,512)(227,511)(228,510)(229,505)(230,508)(231,507)(232,506)(233,529)(234,532)(235,531)(236,530)(237,525)(238,528)(239,527)(240,526)(241,521)(242,524)(243,523)(244,522)(245,517)(246,520)(247,519)(248,518)(249,513)(250,516)(251,515)(252,514)(253,481)(254,484)(255,483)(256,482)(257,477)(258,480)(259,479)(260,478)(261,501)(262,504)(263,503)(264,502)(265,497)(266,500)(267,499)(268,498)(269,493)(270,496)(271,495)(272,494)(273,489)(274,492)(275,491)(276,490)(277,485)(278,488)(279,487)(280,486)(281,733)(282,736)(283,735)(284,734)(285,729)(286,732)(287,731)(288,730)(289,753)(290,756)(291,755)(292,754)(293,749)(294,752)(295,751)(296,750)(297,745)(298,748)(299,747)(300,746)(301,741)(302,744)(303,743)(304,742)(305,737)(306,740)(307,739)(308,738)(309,705)(310,708)(311,707)(312,706)(313,701)(314,704)(315,703)(316,702)(317,725)(318,728)(319,727)(320,726)(321,721)(322,724)(323,723)(324,722)(325,717)(326,720)(327,719)(328,718)(329,713)(330,716)(331,715)(332,714)(333,709)(334,712)(335,711)(336,710)(337,817)(338,820)(339,819)(340,818)(341,813)(342,816)(343,815)(344,814)(345,837)(346,840)(347,839)(348,838)(349,833)(350,836)(351,835)(352,834)(353,829)(354,832)(355,831)(356,830)(357,825)(358,828)(359,827)(360,826)(361,821)(362,824)(363,823)(364,822)(365,789)(366,792)(367,791)(368,790)(369,785)(370,788)(371,787)(372,786)(373,809)(374,812)(375,811)(376,810)(377,805)(378,808)(379,807)(380,806)(381,801)(382,804)(383,803)(384,802)(385,797)(386,800)(387,799)(388,798)(389,793)(390,796)(391,795)(392,794)(393,761)(394,764)(395,763)(396,762)(397,757)(398,760)(399,759)(400,758)(401,781)(402,784)(403,783)(404,782)(405,777)(406,780)(407,779)(408,778)(409,773)(410,776)(411,775)(412,774)(413,769)(414,772)(415,771)(416,770)(417,765)(418,768)(419,767)(420,766);;
s2 := (  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)(833,834)(835,836)(837,838)(839,840);;
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, 
s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(840)!(  3,  4)(  5, 25)(  6, 26)(  7, 28)(  8, 27)(  9, 21)( 10, 22)( 11, 24)( 12, 23)( 13, 17)( 14, 18)( 15, 20)( 16, 19)( 29,113)( 30,114)( 31,116)( 32,115)( 33,137)( 34,138)( 35,140)( 36,139)( 37,133)( 38,134)( 39,136)( 40,135)( 41,129)( 42,130)( 43,132)( 44,131)( 45,125)( 46,126)( 47,128)( 48,127)( 49,121)( 50,122)( 51,124)( 52,123)( 53,117)( 54,118)( 55,120)( 56,119)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61,109)( 62,110)( 63,112)( 64,111)( 65,105)( 66,106)( 67,108)( 68,107)( 69,101)( 70,102)( 71,104)( 72,103)( 73, 97)( 74, 98)( 75,100)( 76, 99)( 77, 93)( 78, 94)( 79, 96)( 80, 95)( 81, 89)( 82, 90)( 83, 92)( 84, 91)(141,281)(142,282)(143,284)(144,283)(145,305)(146,306)(147,308)(148,307)(149,301)(150,302)(151,304)(152,303)(153,297)(154,298)(155,300)(156,299)(157,293)(158,294)(159,296)(160,295)(161,289)(162,290)(163,292)(164,291)(165,285)(166,286)(167,288)(168,287)(169,393)(170,394)(171,396)(172,395)(173,417)(174,418)(175,420)(176,419)(177,413)(178,414)(179,416)(180,415)(181,409)(182,410)(183,412)(184,411)(185,405)(186,406)(187,408)(188,407)(189,401)(190,402)(191,404)(192,403)(193,397)(194,398)(195,400)(196,399)(197,365)(198,366)(199,368)(200,367)(201,389)(202,390)(203,392)(204,391)(205,385)(206,386)(207,388)(208,387)(209,381)(210,382)(211,384)(212,383)(213,377)(214,378)(215,380)(216,379)(217,373)(218,374)(219,376)(220,375)(221,369)(222,370)(223,372)(224,371)(225,337)(226,338)(227,340)(228,339)(229,361)(230,362)(231,364)(232,363)(233,357)(234,358)(235,360)(236,359)(237,353)(238,354)(239,356)(240,355)(241,349)(242,350)(243,352)(244,351)(245,345)(246,346)(247,348)(248,347)(249,341)(250,342)(251,344)(252,343)(253,309)(254,310)(255,312)(256,311)(257,333)(258,334)(259,336)(260,335)(261,329)(262,330)(263,332)(264,331)(265,325)(266,326)(267,328)(268,327)(269,321)(270,322)(271,324)(272,323)(273,317)(274,318)(275,320)(276,319)(277,313)(278,314)(279,316)(280,315)(423,424)(425,445)(426,446)(427,448)(428,447)(429,441)(430,442)(431,444)(432,443)(433,437)(434,438)(435,440)(436,439)(449,533)(450,534)(451,536)(452,535)(453,557)(454,558)(455,560)(456,559)(457,553)(458,554)(459,556)(460,555)(461,549)(462,550)(463,552)(464,551)(465,545)(466,546)(467,548)(468,547)(469,541)(470,542)(471,544)(472,543)(473,537)(474,538)(475,540)(476,539)(477,505)(478,506)(479,508)(480,507)(481,529)(482,530)(483,532)(484,531)(485,525)(486,526)(487,528)(488,527)(489,521)(490,522)(491,524)(492,523)(493,517)(494,518)(495,520)(496,519)(497,513)(498,514)(499,516)(500,515)(501,509)(502,510)(503,512)(504,511)(561,701)(562,702)(563,704)(564,703)(565,725)(566,726)(567,728)(568,727)(569,721)(570,722)(571,724)(572,723)(573,717)(574,718)(575,720)(576,719)(577,713)(578,714)(579,716)(580,715)(581,709)(582,710)(583,712)(584,711)(585,705)(586,706)(587,708)(588,707)(589,813)(590,814)(591,816)(592,815)(593,837)(594,838)(595,840)(596,839)(597,833)(598,834)(599,836)(600,835)(601,829)(602,830)(603,832)(604,831)(605,825)(606,826)(607,828)(608,827)(609,821)(610,822)(611,824)(612,823)(613,817)(614,818)(615,820)(616,819)(617,785)(618,786)(619,788)(620,787)(621,809)(622,810)(623,812)(624,811)(625,805)(626,806)(627,808)(628,807)(629,801)(630,802)(631,804)(632,803)(633,797)(634,798)(635,800)(636,799)(637,793)(638,794)(639,796)(640,795)(641,789)(642,790)(643,792)(644,791)(645,757)(646,758)(647,760)(648,759)(649,781)(650,782)(651,784)(652,783)(653,777)(654,778)(655,780)(656,779)(657,773)(658,774)(659,776)(660,775)(661,769)(662,770)(663,772)(664,771)(665,765)(666,766)(667,768)(668,767)(669,761)(670,762)(671,764)(672,763)(673,729)(674,730)(675,732)(676,731)(677,753)(678,754)(679,756)(680,755)(681,749)(682,750)(683,752)(684,751)(685,745)(686,746)(687,748)(688,747)(689,741)(690,742)(691,744)(692,743)(693,737)(694,738)(695,740)(696,739)(697,733)(698,734)(699,736)(700,735);
s1 := Sym(840)!(  1,593)(  2,596)(  3,595)(  4,594)(  5,589)(  6,592)(  7,591)(  8,590)(  9,613)( 10,616)( 11,615)( 12,614)( 13,609)( 14,612)( 15,611)( 16,610)( 17,605)( 18,608)( 19,607)( 20,606)( 21,601)( 22,604)( 23,603)( 24,602)( 25,597)( 26,600)( 27,599)( 28,598)( 29,565)( 30,568)( 31,567)( 32,566)( 33,561)( 34,564)( 35,563)( 36,562)( 37,585)( 38,588)( 39,587)( 40,586)( 41,581)( 42,584)( 43,583)( 44,582)( 45,577)( 46,580)( 47,579)( 48,578)( 49,573)( 50,576)( 51,575)( 52,574)( 53,569)( 54,572)( 55,571)( 56,570)( 57,677)( 58,680)( 59,679)( 60,678)( 61,673)( 62,676)( 63,675)( 64,674)( 65,697)( 66,700)( 67,699)( 68,698)( 69,693)( 70,696)( 71,695)( 72,694)( 73,689)( 74,692)( 75,691)( 76,690)( 77,685)( 78,688)( 79,687)( 80,686)( 81,681)( 82,684)( 83,683)( 84,682)( 85,649)( 86,652)( 87,651)( 88,650)( 89,645)( 90,648)( 91,647)( 92,646)( 93,669)( 94,672)( 95,671)( 96,670)( 97,665)( 98,668)( 99,667)(100,666)(101,661)(102,664)(103,663)(104,662)(105,657)(106,660)(107,659)(108,658)(109,653)(110,656)(111,655)(112,654)(113,621)(114,624)(115,623)(116,622)(117,617)(118,620)(119,619)(120,618)(121,641)(122,644)(123,643)(124,642)(125,637)(126,640)(127,639)(128,638)(129,633)(130,636)(131,635)(132,634)(133,629)(134,632)(135,631)(136,630)(137,625)(138,628)(139,627)(140,626)(141,453)(142,456)(143,455)(144,454)(145,449)(146,452)(147,451)(148,450)(149,473)(150,476)(151,475)(152,474)(153,469)(154,472)(155,471)(156,470)(157,465)(158,468)(159,467)(160,466)(161,461)(162,464)(163,463)(164,462)(165,457)(166,460)(167,459)(168,458)(169,425)(170,428)(171,427)(172,426)(173,421)(174,424)(175,423)(176,422)(177,445)(178,448)(179,447)(180,446)(181,441)(182,444)(183,443)(184,442)(185,437)(186,440)(187,439)(188,438)(189,433)(190,436)(191,435)(192,434)(193,429)(194,432)(195,431)(196,430)(197,537)(198,540)(199,539)(200,538)(201,533)(202,536)(203,535)(204,534)(205,557)(206,560)(207,559)(208,558)(209,553)(210,556)(211,555)(212,554)(213,549)(214,552)(215,551)(216,550)(217,545)(218,548)(219,547)(220,546)(221,541)(222,544)(223,543)(224,542)(225,509)(226,512)(227,511)(228,510)(229,505)(230,508)(231,507)(232,506)(233,529)(234,532)(235,531)(236,530)(237,525)(238,528)(239,527)(240,526)(241,521)(242,524)(243,523)(244,522)(245,517)(246,520)(247,519)(248,518)(249,513)(250,516)(251,515)(252,514)(253,481)(254,484)(255,483)(256,482)(257,477)(258,480)(259,479)(260,478)(261,501)(262,504)(263,503)(264,502)(265,497)(266,500)(267,499)(268,498)(269,493)(270,496)(271,495)(272,494)(273,489)(274,492)(275,491)(276,490)(277,485)(278,488)(279,487)(280,486)(281,733)(282,736)(283,735)(284,734)(285,729)(286,732)(287,731)(288,730)(289,753)(290,756)(291,755)(292,754)(293,749)(294,752)(295,751)(296,750)(297,745)(298,748)(299,747)(300,746)(301,741)(302,744)(303,743)(304,742)(305,737)(306,740)(307,739)(308,738)(309,705)(310,708)(311,707)(312,706)(313,701)(314,704)(315,703)(316,702)(317,725)(318,728)(319,727)(320,726)(321,721)(322,724)(323,723)(324,722)(325,717)(326,720)(327,719)(328,718)(329,713)(330,716)(331,715)(332,714)(333,709)(334,712)(335,711)(336,710)(337,817)(338,820)(339,819)(340,818)(341,813)(342,816)(343,815)(344,814)(345,837)(346,840)(347,839)(348,838)(349,833)(350,836)(351,835)(352,834)(353,829)(354,832)(355,831)(356,830)(357,825)(358,828)(359,827)(360,826)(361,821)(362,824)(363,823)(364,822)(365,789)(366,792)(367,791)(368,790)(369,785)(370,788)(371,787)(372,786)(373,809)(374,812)(375,811)(376,810)(377,805)(378,808)(379,807)(380,806)(381,801)(382,804)(383,803)(384,802)(385,797)(386,800)(387,799)(388,798)(389,793)(390,796)(391,795)(392,794)(393,761)(394,764)(395,763)(396,762)(397,757)(398,760)(399,759)(400,758)(401,781)(402,784)(403,783)(404,782)(405,777)(406,780)(407,779)(408,778)(409,773)(410,776)(411,775)(412,774)(413,769)(414,772)(415,771)(416,770)(417,765)(418,768)(419,767)(420,766);
s2 := Sym(840)!(  1,  2)(  3,  4)(  5,  6)(  7,  8)(  9, 10)( 11, 12)( 13, 14)( 15, 16)( 17, 18)( 19, 20)( 21, 22)( 23, 24)( 25, 26)( 27, 28)( 29, 30)( 31, 32)( 33, 34)( 35, 36)( 37, 38)( 39, 40)( 41, 42)( 43, 44)( 45, 46)( 47, 48)( 49, 50)( 51, 52)( 53, 54)( 55, 56)( 57, 58)( 59, 60)( 61, 62)( 63, 64)( 65, 66)( 67, 68)( 69, 70)( 71, 72)( 73, 74)( 75, 76)( 77, 78)( 79, 80)( 81, 82)( 83, 84)( 85, 86)( 87, 88)( 89, 90)( 91, 92)( 93, 94)( 95, 96)( 97, 98)( 99,100)(101,102)(103,104)(105,106)(107,108)(109,110)(111,112)(113,114)(115,116)(117,118)(119,120)(121,122)(123,124)(125,126)(127,128)(129,130)(131,132)(133,134)(135,136)(137,138)(139,140)(141,142)(143,144)(145,146)(147,148)(149,150)(151,152)(153,154)(155,156)(157,158)(159,160)(161,162)(163,164)(165,166)(167,168)(169,170)(171,172)(173,174)(175,176)(177,178)(179,180)(181,182)(183,184)(185,186)(187,188)(189,190)(191,192)(193,194)(195,196)(197,198)(199,200)(201,202)(203,204)(205,206)(207,208)(209,210)(211,212)(213,214)(215,216)(217,218)(219,220)(221,222)(223,224)(225,226)(227,228)(229,230)(231,232)(233,234)(235,236)(237,238)(239,240)(241,242)(243,244)(245,246)(247,248)(249,250)(251,252)(253,254)(255,256)(257,258)(259,260)(261,262)(263,264)(265,266)(267,268)(269,270)(271,272)(273,274)(275,276)(277,278)(279,280)(281,282)(283,284)(285,286)(287,288)(289,290)(291,292)(293,294)(295,296)(297,298)(299,300)(301,302)(303,304)(305,306)(307,308)(309,310)(311,312)(313,314)(315,316)(317,318)(319,320)(321,322)(323,324)(325,326)(327,328)(329,330)(331,332)(333,334)(335,336)(337,338)(339,340)(341,342)(343,344)(345,346)(347,348)(349,350)(351,352)(353,354)(355,356)(357,358)(359,360)(361,362)(363,364)(365,366)(367,368)(369,370)(371,372)(373,374)(375,376)(377,378)(379,380)(381,382)(383,384)(385,386)(387,388)(389,390)(391,392)(393,394)(395,396)(397,398)(399,400)(401,402)(403,404)(405,406)(407,408)(409,410)(411,412)(413,414)(415,416)(417,418)(419,420)(421,422)(423,424)(425,426)(427,428)(429,430)(431,432)(433,434)(435,436)(437,438)(439,440)(441,442)(443,444)(445,446)(447,448)(449,450)(451,452)(453,454)(455,456)(457,458)(459,460)(461,462)(463,464)(465,466)(467,468)(469,470)(471,472)(473,474)(475,476)(477,478)(479,480)(481,482)(483,484)(485,486)(487,488)(489,490)(491,492)(493,494)(495,496)(497,498)(499,500)(501,502)(503,504)(505,506)(507,508)(509,510)(511,512)(513,514)(515,516)(517,518)(519,520)(521,522)(523,524)(525,526)(527,528)(529,530)(531,532)(533,534)(535,536)(537,538)(539,540)(541,542)(543,544)(545,546)(547,548)(549,550)(551,552)(553,554)(555,556)(557,558)(559,560)(561,562)(563,564)(565,566)(567,568)(569,570)(571,572)(573,574)(575,576)(577,578)(579,580)(581,582)(583,584)(585,586)(587,588)(589,590)(591,592)(593,594)(595,596)(597,598)(599,600)(601,602)(603,604)(605,606)(607,608)(609,610)(611,612)(613,614)(615,616)(617,618)(619,620)(621,622)(623,624)(625,626)(627,628)(629,630)(631,632)(633,634)(635,636)(637,638)(639,640)(641,642)(643,644)(645,646)(647,648)(649,650)(651,652)(653,654)(655,656)(657,658)(659,660)(661,662)(663,664)(665,666)(667,668)(669,670)(671,672)(673,674)(675,676)(677,678)(679,680)(681,682)(683,684)(685,686)(687,688)(689,690)(691,692)(693,694)(695,696)(697,698)(699,700)(701,702)(703,704)(705,706)(707,708)(709,710)(711,712)(713,714)(715,716)(717,718)(719,720)(721,722)(723,724)(725,726)(727,728)(729,730)(731,732)(733,734)(735,736)(737,738)(739,740)(741,742)(743,744)(745,746)(747,748)(749,750)(751,752)(753,754)(755,756)(757,758)(759,760)(761,762)(763,764)(765,766)(767,768)(769,770)(771,772)(773,774)(775,776)(777,778)(779,780)(781,782)(783,784)(785,786)(787,788)(789,790)(791,792)(793,794)(795,796)(797,798)(799,800)(801,802)(803,804)(805,806)(807,808)(809,810)(811,812)(813,814)(815,816)(817,818)(819,820)(821,822)(823,824)(825,826)(827,828)(829,830)(831,832)(833,834)(835,836)(837,838)(839,840);
poly := sub<Sym(840)|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, 
s2*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*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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