Polytope of Type {10,64}

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