Polytope of Type {40,16}

Play with this polytope as a twisty puzzle

s0 := (  1,161)(  2,165)(  3,164)(  4,163)(  5,162)(  6,166)(  7,170)(  8,169)(  9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)( 16,176)( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)( 24,183)( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)( 32,195)( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)( 40,197)( 41,211)( 42,215)( 43,214)( 44,213)( 45,212)( 46,216)( 47,220)( 48,219)( 49,218)( 50,217)( 51,201)( 52,205)( 53,204)( 54,203)( 55,202)( 56,206)( 57,210)( 58,209)( 59,208)( 60,207)( 61,231)( 62,235)( 63,234)( 64,233)( 65,232)( 66,236)( 67,240)( 68,239)( 69,238)( 70,237)( 71,221)( 72,225)( 73,224)( 74,223)( 75,222)( 76,226)( 77,230)( 78,229)( 79,228)( 80,227)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,256)( 87,260)( 88,259)( 89,258)( 90,257)( 91,241)( 92,245)( 93,244)( 94,243)( 95,242)( 96,246)( 97,250)( 98,249)( 99,248)(100,247)(101,271)(102,275)(103,274)(104,273)(105,272)(106,276)(107,280)(108,279)(109,278)(110,277)(111,261)(112,265)(113,264)(114,263)(115,262)(116,266)(117,270)(118,269)(119,268)(120,267)(121,281)(122,285)(123,284)(124,283)(125,282)(126,286)(127,290)(128,289)(129,288)(130,287)(131,291)(132,295)(133,294)(134,293)(135,292)(136,296)(137,300)(138,299)(139,298)(140,297)(141,301)(142,305)(143,304)(144,303)(145,302)(146,306)(147,310)(148,309)(149,308)(150,307)(151,311)(152,315)(153,314)(154,313)(155,312)(156,316)(157,320)(158,319)(159,318)(160,317)(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)(328,489)(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)(336,496)(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)(344,503)(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)(352,515)(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)(360,517)(361,531)(362,535)(363,534)(364,533)(365,532)(366,536)(367,540)(368,539)(369,538)(370,537)(371,521)(372,525)(373,524)(374,523)(375,522)(376,526)(377,530)(378,529)(379,528)(380,527)(381,551)(382,555)(383,554)(384,553)(385,552)(386,556)(387,560)(388,559)(389,558)(390,557)(391,541)(392,545)(393,544)(394,543)(395,542)(396,546)(397,550)(398,549)(399,548)(400,547)(401,571)(402,575)(403,574)(404,573)(405,572)(406,576)(407,580)(408,579)(409,578)(410,577)(411,561)(412,565)(413,564)(414,563)(415,562)(416,566)(417,570)(418,569)(419,568)(420,567)(421,591)(422,595)(423,594)(424,593)(425,592)(426,596)(427,600)(428,599)(429,598)(430,597)(431,581)(432,585)(433,584)(434,583)(435,582)(436,586)(437,590)(438,589)(439,588)(440,587)(441,601)(442,605)(443,604)(444,603)(445,602)(446,606)(447,610)(448,609)(449,608)(450,607)(451,611)(452,615)(453,614)(454,613)(455,612)(456,616)(457,620)(458,619)(459,618)(460,617)(461,621)(462,625)(463,624)(464,623)(465,622)(466,626)(467,630)(468,629)(469,628)(470,627)(471,631)(472,635)(473,634)(474,633)(475,632)(476,636)(477,640)(478,639)(479,638)(480,637);;
s1 := (  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 38)( 32, 37)( 33, 36)( 34, 40)( 35, 39)( 41, 53)( 42, 52)( 43, 51)( 44, 55)( 45, 54)( 46, 58)( 47, 57)( 48, 56)( 49, 60)( 50, 59)( 61, 78)( 62, 77)( 63, 76)( 64, 80)( 65, 79)( 66, 73)( 67, 72)( 68, 71)( 69, 75)( 70, 74)( 81,103)( 82,102)( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,113)( 92,112)( 93,111)( 94,115)( 95,114)( 96,118)( 97,117)( 98,116)( 99,120)(100,119)(121,153)(122,152)(123,151)(124,155)(125,154)(126,158)(127,157)(128,156)(129,160)(130,159)(131,143)(132,142)(133,141)(134,145)(135,144)(136,148)(137,147)(138,146)(139,150)(140,149)(161,203)(162,202)(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,213)(172,212)(173,211)(174,215)(175,214)(176,218)(177,217)(178,216)(179,220)(180,219)(181,228)(182,227)(183,226)(184,230)(185,229)(186,223)(187,222)(188,221)(189,225)(190,224)(191,238)(192,237)(193,236)(194,240)(195,239)(196,233)(197,232)(198,231)(199,235)(200,234)(241,303)(242,302)(243,301)(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)(260,319)(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)(268,286)(269,290)(270,289)(271,293)(272,292)(273,291)(274,295)(275,294)(276,298)(277,297)(278,296)(279,300)(280,299)(321,403)(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)(331,413)(332,412)(333,411)(334,415)(335,414)(336,418)(337,417)(338,416)(339,420)(340,419)(341,428)(342,427)(343,426)(344,430)(345,429)(346,423)(347,422)(348,421)(349,425)(350,424)(351,438)(352,437)(353,436)(354,440)(355,439)(356,433)(357,432)(358,431)(359,435)(360,434)(361,453)(362,452)(363,451)(364,455)(365,454)(366,458)(367,457)(368,456)(369,460)(370,459)(371,443)(372,442)(373,441)(374,445)(375,444)(376,448)(377,447)(378,446)(379,450)(380,449)(381,478)(382,477)(383,476)(384,480)(385,479)(386,473)(387,472)(388,471)(389,475)(390,474)(391,468)(392,467)(393,466)(394,470)(395,469)(396,463)(397,462)(398,461)(399,465)(400,464)(481,613)(482,612)(483,611)(484,615)(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,603)(492,602)(493,601)(494,605)(495,604)(496,608)(497,607)(498,606)(499,610)(500,609)(501,638)(502,637)(503,636)(504,640)(505,639)(506,633)(507,632)(508,631)(509,635)(510,634)(511,628)(512,627)(513,626)(514,630)(515,629)(516,623)(517,622)(518,621)(519,625)(520,624)(521,573)(522,572)(523,571)(524,575)(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,563)(532,562)(533,561)(534,565)(535,564)(536,568)(537,567)(538,566)(539,570)(540,569)(541,598)(542,597)(543,596)(544,600)(545,599)(546,593)(547,592)(548,591)(549,595)(550,594)(551,588)(552,587)(553,586)(554,590)(555,589)(556,583)(557,582)(558,581)(559,585)(560,584);;
s2 := (  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)(  8,488)(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,506)( 22,507)( 23,508)( 24,509)( 25,510)( 26,501)( 27,502)( 28,503)( 29,504)( 30,505)( 31,516)( 32,517)( 33,518)( 34,519)( 35,520)( 36,511)( 37,512)( 38,513)( 39,514)( 40,515)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,546)( 62,547)( 63,548)( 64,549)( 65,550)( 66,541)( 67,542)( 68,543)( 69,544)( 70,545)( 71,556)( 72,557)( 73,558)( 74,559)( 75,560)( 76,551)( 77,552)( 78,553)( 79,554)( 80,555)( 81,591)( 82,592)( 83,593)( 84,594)( 85,595)( 86,596)( 87,597)( 88,598)( 89,599)( 90,600)( 91,581)( 92,582)( 93,583)( 94,584)( 95,585)( 96,586)( 97,587)( 98,588)( 99,589)(100,590)(101,571)(102,572)(103,573)(104,574)(105,575)(106,576)(107,577)(108,578)(109,579)(110,580)(111,561)(112,562)(113,563)(114,564)(115,565)(116,566)(117,567)(118,568)(119,569)(120,570)(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)(129,639)(130,640)(131,621)(132,622)(133,623)(134,624)(135,625)(136,626)(137,627)(138,628)(139,629)(140,630)(141,611)(142,612)(143,613)(144,614)(145,615)(146,616)(147,617)(148,618)(149,619)(150,620)(151,601)(152,602)(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)(161,321)(162,322)(163,323)(164,324)(165,325)(166,326)(167,327)(168,328)(169,329)(170,330)(171,331)(172,332)(173,333)(174,334)(175,335)(176,336)(177,337)(178,338)(179,339)(180,340)(181,346)(182,347)(183,348)(184,349)(185,350)(186,341)(187,342)(188,343)(189,344)(190,345)(191,356)(192,357)(193,358)(194,359)(195,360)(196,351)(197,352)(198,353)(199,354)(200,355)(201,361)(202,362)(203,363)(204,364)(205,365)(206,366)(207,367)(208,368)(209,369)(210,370)(211,371)(212,372)(213,373)(214,374)(215,375)(216,376)(217,377)(218,378)(219,379)(220,380)(221,386)(222,387)(223,388)(224,389)(225,390)(226,381)(227,382)(228,383)(229,384)(230,385)(231,396)(232,397)(233,398)(234,399)(235,400)(236,391)(237,392)(238,393)(239,394)(240,395)(241,431)(242,432)(243,433)(244,434)(245,435)(246,436)(247,437)(248,438)(249,439)(250,440)(251,421)(252,422)(253,423)(254,424)(255,425)(256,426)(257,427)(258,428)(259,429)(260,430)(261,411)(262,412)(263,413)(264,414)(265,415)(266,416)(267,417)(268,418)(269,419)(270,420)(271,401)(272,402)(273,403)(274,404)(275,405)(276,406)(277,407)(278,408)(279,409)(280,410)(281,471)(282,472)(283,473)(284,474)(285,475)(286,476)(287,477)(288,478)(289,479)(290,480)(291,461)(292,462)(293,463)(294,464)(295,465)(296,466)(297,467)(298,468)(299,469)(300,470)(301,451)(302,452)(303,453)(304,454)(305,455)(306,456)(307,457)(308,458)(309,459)(310,460)(311,441)(312,442)(313,443)(314,444)(315,445)(316,446)(317,447)(318,448)(319,449)(320,450);;
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, 
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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(640)!(  1,161)(  2,165)(  3,164)(  4,163)(  5,162)(  6,166)(  7,170)(  8,169)(  9,168)( 10,167)( 11,171)( 12,175)( 13,174)( 14,173)( 15,172)( 16,176)( 17,180)( 18,179)( 19,178)( 20,177)( 21,181)( 22,185)( 23,184)( 24,183)( 25,182)( 26,186)( 27,190)( 28,189)( 29,188)( 30,187)( 31,191)( 32,195)( 33,194)( 34,193)( 35,192)( 36,196)( 37,200)( 38,199)( 39,198)( 40,197)( 41,211)( 42,215)( 43,214)( 44,213)( 45,212)( 46,216)( 47,220)( 48,219)( 49,218)( 50,217)( 51,201)( 52,205)( 53,204)( 54,203)( 55,202)( 56,206)( 57,210)( 58,209)( 59,208)( 60,207)( 61,231)( 62,235)( 63,234)( 64,233)( 65,232)( 66,236)( 67,240)( 68,239)( 69,238)( 70,237)( 71,221)( 72,225)( 73,224)( 74,223)( 75,222)( 76,226)( 77,230)( 78,229)( 79,228)( 80,227)( 81,251)( 82,255)( 83,254)( 84,253)( 85,252)( 86,256)( 87,260)( 88,259)( 89,258)( 90,257)( 91,241)( 92,245)( 93,244)( 94,243)( 95,242)( 96,246)( 97,250)( 98,249)( 99,248)(100,247)(101,271)(102,275)(103,274)(104,273)(105,272)(106,276)(107,280)(108,279)(109,278)(110,277)(111,261)(112,265)(113,264)(114,263)(115,262)(116,266)(117,270)(118,269)(119,268)(120,267)(121,281)(122,285)(123,284)(124,283)(125,282)(126,286)(127,290)(128,289)(129,288)(130,287)(131,291)(132,295)(133,294)(134,293)(135,292)(136,296)(137,300)(138,299)(139,298)(140,297)(141,301)(142,305)(143,304)(144,303)(145,302)(146,306)(147,310)(148,309)(149,308)(150,307)(151,311)(152,315)(153,314)(154,313)(155,312)(156,316)(157,320)(158,319)(159,318)(160,317)(321,481)(322,485)(323,484)(324,483)(325,482)(326,486)(327,490)(328,489)(329,488)(330,487)(331,491)(332,495)(333,494)(334,493)(335,492)(336,496)(337,500)(338,499)(339,498)(340,497)(341,501)(342,505)(343,504)(344,503)(345,502)(346,506)(347,510)(348,509)(349,508)(350,507)(351,511)(352,515)(353,514)(354,513)(355,512)(356,516)(357,520)(358,519)(359,518)(360,517)(361,531)(362,535)(363,534)(364,533)(365,532)(366,536)(367,540)(368,539)(369,538)(370,537)(371,521)(372,525)(373,524)(374,523)(375,522)(376,526)(377,530)(378,529)(379,528)(380,527)(381,551)(382,555)(383,554)(384,553)(385,552)(386,556)(387,560)(388,559)(389,558)(390,557)(391,541)(392,545)(393,544)(394,543)(395,542)(396,546)(397,550)(398,549)(399,548)(400,547)(401,571)(402,575)(403,574)(404,573)(405,572)(406,576)(407,580)(408,579)(409,578)(410,577)(411,561)(412,565)(413,564)(414,563)(415,562)(416,566)(417,570)(418,569)(419,568)(420,567)(421,591)(422,595)(423,594)(424,593)(425,592)(426,596)(427,600)(428,599)(429,598)(430,597)(431,581)(432,585)(433,584)(434,583)(435,582)(436,586)(437,590)(438,589)(439,588)(440,587)(441,601)(442,605)(443,604)(444,603)(445,602)(446,606)(447,610)(448,609)(449,608)(450,607)(451,611)(452,615)(453,614)(454,613)(455,612)(456,616)(457,620)(458,619)(459,618)(460,617)(461,621)(462,625)(463,624)(464,623)(465,622)(466,626)(467,630)(468,629)(469,628)(470,627)(471,631)(472,635)(473,634)(474,633)(475,632)(476,636)(477,640)(478,639)(479,638)(480,637);
s1 := Sym(640)!(  1,  3)(  4,  5)(  6,  8)(  9, 10)( 11, 13)( 14, 15)( 16, 18)( 19, 20)( 21, 28)( 22, 27)( 23, 26)( 24, 30)( 25, 29)( 31, 38)( 32, 37)( 33, 36)( 34, 40)( 35, 39)( 41, 53)( 42, 52)( 43, 51)( 44, 55)( 45, 54)( 46, 58)( 47, 57)( 48, 56)( 49, 60)( 50, 59)( 61, 78)( 62, 77)( 63, 76)( 64, 80)( 65, 79)( 66, 73)( 67, 72)( 68, 71)( 69, 75)( 70, 74)( 81,103)( 82,102)( 83,101)( 84,105)( 85,104)( 86,108)( 87,107)( 88,106)( 89,110)( 90,109)( 91,113)( 92,112)( 93,111)( 94,115)( 95,114)( 96,118)( 97,117)( 98,116)( 99,120)(100,119)(121,153)(122,152)(123,151)(124,155)(125,154)(126,158)(127,157)(128,156)(129,160)(130,159)(131,143)(132,142)(133,141)(134,145)(135,144)(136,148)(137,147)(138,146)(139,150)(140,149)(161,203)(162,202)(163,201)(164,205)(165,204)(166,208)(167,207)(168,206)(169,210)(170,209)(171,213)(172,212)(173,211)(174,215)(175,214)(176,218)(177,217)(178,216)(179,220)(180,219)(181,228)(182,227)(183,226)(184,230)(185,229)(186,223)(187,222)(188,221)(189,225)(190,224)(191,238)(192,237)(193,236)(194,240)(195,239)(196,233)(197,232)(198,231)(199,235)(200,234)(241,303)(242,302)(243,301)(244,305)(245,304)(246,308)(247,307)(248,306)(249,310)(250,309)(251,313)(252,312)(253,311)(254,315)(255,314)(256,318)(257,317)(258,316)(259,320)(260,319)(261,283)(262,282)(263,281)(264,285)(265,284)(266,288)(267,287)(268,286)(269,290)(270,289)(271,293)(272,292)(273,291)(274,295)(275,294)(276,298)(277,297)(278,296)(279,300)(280,299)(321,403)(322,402)(323,401)(324,405)(325,404)(326,408)(327,407)(328,406)(329,410)(330,409)(331,413)(332,412)(333,411)(334,415)(335,414)(336,418)(337,417)(338,416)(339,420)(340,419)(341,428)(342,427)(343,426)(344,430)(345,429)(346,423)(347,422)(348,421)(349,425)(350,424)(351,438)(352,437)(353,436)(354,440)(355,439)(356,433)(357,432)(358,431)(359,435)(360,434)(361,453)(362,452)(363,451)(364,455)(365,454)(366,458)(367,457)(368,456)(369,460)(370,459)(371,443)(372,442)(373,441)(374,445)(375,444)(376,448)(377,447)(378,446)(379,450)(380,449)(381,478)(382,477)(383,476)(384,480)(385,479)(386,473)(387,472)(388,471)(389,475)(390,474)(391,468)(392,467)(393,466)(394,470)(395,469)(396,463)(397,462)(398,461)(399,465)(400,464)(481,613)(482,612)(483,611)(484,615)(485,614)(486,618)(487,617)(488,616)(489,620)(490,619)(491,603)(492,602)(493,601)(494,605)(495,604)(496,608)(497,607)(498,606)(499,610)(500,609)(501,638)(502,637)(503,636)(504,640)(505,639)(506,633)(507,632)(508,631)(509,635)(510,634)(511,628)(512,627)(513,626)(514,630)(515,629)(516,623)(517,622)(518,621)(519,625)(520,624)(521,573)(522,572)(523,571)(524,575)(525,574)(526,578)(527,577)(528,576)(529,580)(530,579)(531,563)(532,562)(533,561)(534,565)(535,564)(536,568)(537,567)(538,566)(539,570)(540,569)(541,598)(542,597)(543,596)(544,600)(545,599)(546,593)(547,592)(548,591)(549,595)(550,594)(551,588)(552,587)(553,586)(554,590)(555,589)(556,583)(557,582)(558,581)(559,585)(560,584);
s2 := Sym(640)!(  1,481)(  2,482)(  3,483)(  4,484)(  5,485)(  6,486)(  7,487)(  8,488)(  9,489)( 10,490)( 11,491)( 12,492)( 13,493)( 14,494)( 15,495)( 16,496)( 17,497)( 18,498)( 19,499)( 20,500)( 21,506)( 22,507)( 23,508)( 24,509)( 25,510)( 26,501)( 27,502)( 28,503)( 29,504)( 30,505)( 31,516)( 32,517)( 33,518)( 34,519)( 35,520)( 36,511)( 37,512)( 38,513)( 39,514)( 40,515)( 41,521)( 42,522)( 43,523)( 44,524)( 45,525)( 46,526)( 47,527)( 48,528)( 49,529)( 50,530)( 51,531)( 52,532)( 53,533)( 54,534)( 55,535)( 56,536)( 57,537)( 58,538)( 59,539)( 60,540)( 61,546)( 62,547)( 63,548)( 64,549)( 65,550)( 66,541)( 67,542)( 68,543)( 69,544)( 70,545)( 71,556)( 72,557)( 73,558)( 74,559)( 75,560)( 76,551)( 77,552)( 78,553)( 79,554)( 80,555)( 81,591)( 82,592)( 83,593)( 84,594)( 85,595)( 86,596)( 87,597)( 88,598)( 89,599)( 90,600)( 91,581)( 92,582)( 93,583)( 94,584)( 95,585)( 96,586)( 97,587)( 98,588)( 99,589)(100,590)(101,571)(102,572)(103,573)(104,574)(105,575)(106,576)(107,577)(108,578)(109,579)(110,580)(111,561)(112,562)(113,563)(114,564)(115,565)(116,566)(117,567)(118,568)(119,569)(120,570)(121,631)(122,632)(123,633)(124,634)(125,635)(126,636)(127,637)(128,638)(129,639)(130,640)(131,621)(132,622)(133,623)(134,624)(135,625)(136,626)(137,627)(138,628)(139,629)(140,630)(141,611)(142,612)(143,613)(144,614)(145,615)(146,616)(147,617)(148,618)(149,619)(150,620)(151,601)(152,602)(153,603)(154,604)(155,605)(156,606)(157,607)(158,608)(159,609)(160,610)(161,321)(162,322)(163,323)(164,324)(165,325)(166,326)(167,327)(168,328)(169,329)(170,330)(171,331)(172,332)(173,333)(174,334)(175,335)(176,336)(177,337)(178,338)(179,339)(180,340)(181,346)(182,347)(183,348)(184,349)(185,350)(186,341)(187,342)(188,343)(189,344)(190,345)(191,356)(192,357)(193,358)(194,359)(195,360)(196,351)(197,352)(198,353)(199,354)(200,355)(201,361)(202,362)(203,363)(204,364)(205,365)(206,366)(207,367)(208,368)(209,369)(210,370)(211,371)(212,372)(213,373)(214,374)(215,375)(216,376)(217,377)(218,378)(219,379)(220,380)(221,386)(222,387)(223,388)(224,389)(225,390)(226,381)(227,382)(228,383)(229,384)(230,385)(231,396)(232,397)(233,398)(234,399)(235,400)(236,391)(237,392)(238,393)(239,394)(240,395)(241,431)(242,432)(243,433)(244,434)(245,435)(246,436)(247,437)(248,438)(249,439)(250,440)(251,421)(252,422)(253,423)(254,424)(255,425)(256,426)(257,427)(258,428)(259,429)(260,430)(261,411)(262,412)(263,413)(264,414)(265,415)(266,416)(267,417)(268,418)(269,419)(270,420)(271,401)(272,402)(273,403)(274,404)(275,405)(276,406)(277,407)(278,408)(279,409)(280,410)(281,471)(282,472)(283,473)(284,474)(285,475)(286,476)(287,477)(288,478)(289,479)(290,480)(291,461)(292,462)(293,463)(294,464)(295,465)(296,466)(297,467)(298,468)(299,469)(300,470)(301,451)(302,452)(303,453)(304,454)(305,455)(306,456)(307,457)(308,458)(309,459)(310,460)(311,441)(312,442)(313,443)(314,444)(315,445)(316,446)(317,447)(318,448)(319,449)(320,450);
poly := sub<Sym(640)|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, 
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, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*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