Polytope of Type {162,4}

Play with this polytope as a twisty puzzle

s0 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(109,321)(110,322)(111,324)(112,323)(113,317)(114,318)(115,320)(116,319)(117,313)(118,314)(119,316)(120,315)(121,309)(122,310)(123,312)(124,311)(125,305)(126,306)(127,308)(128,307)(129,301)(130,302)(131,304)(132,303)(133,297)(134,298)(135,300)(136,299)(137,293)(138,294)(139,296)(140,295)(141,289)(142,290)(143,292)(144,291)(145,285)(146,286)(147,288)(148,287)(149,281)(150,282)(151,284)(152,283)(153,277)(154,278)(155,280)(156,279)(157,273)(158,274)(159,276)(160,275)(161,269)(162,270)(163,272)(164,271)(165,265)(166,266)(167,268)(168,267)(169,261)(170,262)(171,264)(172,263)(173,257)(174,258)(175,260)(176,259)(177,253)(178,254)(179,256)(180,255)(181,249)(182,250)(183,252)(184,251)(185,245)(186,246)(187,248)(188,247)(189,241)(190,242)(191,244)(192,243)(193,237)(194,238)(195,240)(196,239)(197,233)(198,234)(199,236)(200,235)(201,229)(202,230)(203,232)(204,231)(205,225)(206,226)(207,228)(208,227)(209,221)(210,222)(211,224)(212,223)(213,217)(214,218)(215,220)(216,219)(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)(338,358)(339,360)(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)(346,350)(347,352)(348,351)(361,429)(362,430)(363,432)(364,431)(365,425)(366,426)(367,428)(368,427)(369,421)(370,422)(371,424)(372,423)(373,417)(374,418)(375,420)(376,419)(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)(384,411)(385,405)(386,406)(387,408)(388,407)(389,401)(390,402)(391,404)(392,403)(393,397)(394,398)(395,400)(396,399)(433,645)(434,646)(435,648)(436,647)(437,641)(438,642)(439,644)(440,643)(441,637)(442,638)(443,640)(444,639)(445,633)(446,634)(447,636)(448,635)(449,629)(450,630)(451,632)(452,631)(453,625)(454,626)(455,628)(456,627)(457,621)(458,622)(459,624)(460,623)(461,617)(462,618)(463,620)(464,619)(465,613)(466,614)(467,616)(468,615)(469,609)(470,610)(471,612)(472,611)(473,605)(474,606)(475,608)(476,607)(477,601)(478,602)(479,604)(480,603)(481,597)(482,598)(483,600)(484,599)(485,593)(486,594)(487,596)(488,595)(489,589)(490,590)(491,592)(492,591)(493,585)(494,586)(495,588)(496,587)(497,581)(498,582)(499,584)(500,583)(501,577)(502,578)(503,580)(504,579)(505,573)(506,574)(507,576)(508,575)(509,569)(510,570)(511,572)(512,571)(513,565)(514,566)(515,568)(516,567)(517,561)(518,562)(519,564)(520,563)(521,557)(522,558)(523,560)(524,559)(525,553)(526,554)(527,556)(528,555)(529,549)(530,550)(531,552)(532,551)(533,545)(534,546)(535,548)(536,547)(537,541)(538,542)(539,544)(540,543);;
s1 := (  1,433)(  2,436)(  3,435)(  4,434)(  5,441)(  6,444)(  7,443)(  8,442)(  9,437)( 10,440)( 11,439)( 12,438)( 13,465)( 14,468)( 15,467)( 16,466)( 17,461)( 18,464)( 19,463)( 20,462)( 21,457)( 22,460)( 23,459)( 24,458)( 25,453)( 26,456)( 27,455)( 28,454)( 29,449)( 30,452)( 31,451)( 32,450)( 33,445)( 34,448)( 35,447)( 36,446)( 37,537)( 38,540)( 39,539)( 40,538)( 41,533)( 42,536)( 43,535)( 44,534)( 45,529)( 46,532)( 47,531)( 48,530)( 49,525)( 50,528)( 51,527)( 52,526)( 53,521)( 54,524)( 55,523)( 56,522)( 57,517)( 58,520)( 59,519)( 60,518)( 61,513)( 62,516)( 63,515)( 64,514)( 65,509)( 66,512)( 67,511)( 68,510)( 69,505)( 70,508)( 71,507)( 72,506)( 73,501)( 74,504)( 75,503)( 76,502)( 77,497)( 78,500)( 79,499)( 80,498)( 81,493)( 82,496)( 83,495)( 84,494)( 85,489)( 86,492)( 87,491)( 88,490)( 89,485)( 90,488)( 91,487)( 92,486)( 93,481)( 94,484)( 95,483)( 96,482)( 97,477)( 98,480)( 99,479)(100,478)(101,473)(102,476)(103,475)(104,474)(105,469)(106,472)(107,471)(108,470)(109,325)(110,328)(111,327)(112,326)(113,333)(114,336)(115,335)(116,334)(117,329)(118,332)(119,331)(120,330)(121,357)(122,360)(123,359)(124,358)(125,353)(126,356)(127,355)(128,354)(129,349)(130,352)(131,351)(132,350)(133,345)(134,348)(135,347)(136,346)(137,341)(138,344)(139,343)(140,342)(141,337)(142,340)(143,339)(144,338)(145,429)(146,432)(147,431)(148,430)(149,425)(150,428)(151,427)(152,426)(153,421)(154,424)(155,423)(156,422)(157,417)(158,420)(159,419)(160,418)(161,413)(162,416)(163,415)(164,414)(165,409)(166,412)(167,411)(168,410)(169,405)(170,408)(171,407)(172,406)(173,401)(174,404)(175,403)(176,402)(177,397)(178,400)(179,399)(180,398)(181,393)(182,396)(183,395)(184,394)(185,389)(186,392)(187,391)(188,390)(189,385)(190,388)(191,387)(192,386)(193,381)(194,384)(195,383)(196,382)(197,377)(198,380)(199,379)(200,378)(201,373)(202,376)(203,375)(204,374)(205,369)(206,372)(207,371)(208,370)(209,365)(210,368)(211,367)(212,366)(213,361)(214,364)(215,363)(216,362)(217,645)(218,648)(219,647)(220,646)(221,641)(222,644)(223,643)(224,642)(225,637)(226,640)(227,639)(228,638)(229,633)(230,636)(231,635)(232,634)(233,629)(234,632)(235,631)(236,630)(237,625)(238,628)(239,627)(240,626)(241,621)(242,624)(243,623)(244,622)(245,617)(246,620)(247,619)(248,618)(249,613)(250,616)(251,615)(252,614)(253,609)(254,612)(255,611)(256,610)(257,605)(258,608)(259,607)(260,606)(261,601)(262,604)(263,603)(264,602)(265,597)(266,600)(267,599)(268,598)(269,593)(270,596)(271,595)(272,594)(273,589)(274,592)(275,591)(276,590)(277,585)(278,588)(279,587)(280,586)(281,581)(282,584)(283,583)(284,582)(285,577)(286,580)(287,579)(288,578)(289,573)(290,576)(291,575)(292,574)(293,569)(294,572)(295,571)(296,570)(297,565)(298,568)(299,567)(300,566)(301,561)(302,564)(303,563)(304,562)(305,557)(306,560)(307,559)(308,558)(309,553)(310,556)(311,555)(312,554)(313,549)(314,552)(315,551)(316,550)(317,545)(318,548)(319,547)(320,546)(321,541)(322,544)(323,543)(324,542);;
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);;
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 ];;
poly := F / rels;;
 

s0 := Sym(648)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 33)( 14, 34)( 15, 36)( 16, 35)( 17, 29)( 18, 30)( 19, 32)( 20, 31)( 21, 25)( 22, 26)( 23, 28)( 24, 27)( 37,105)( 38,106)( 39,108)( 40,107)( 41,101)( 42,102)( 43,104)( 44,103)( 45, 97)( 46, 98)( 47,100)( 48, 99)( 49, 93)( 50, 94)( 51, 96)( 52, 95)( 53, 89)( 54, 90)( 55, 92)( 56, 91)( 57, 85)( 58, 86)( 59, 88)( 60, 87)( 61, 81)( 62, 82)( 63, 84)( 64, 83)( 65, 77)( 66, 78)( 67, 80)( 68, 79)( 69, 73)( 70, 74)( 71, 76)( 72, 75)(109,321)(110,322)(111,324)(112,323)(113,317)(114,318)(115,320)(116,319)(117,313)(118,314)(119,316)(120,315)(121,309)(122,310)(123,312)(124,311)(125,305)(126,306)(127,308)(128,307)(129,301)(130,302)(131,304)(132,303)(133,297)(134,298)(135,300)(136,299)(137,293)(138,294)(139,296)(140,295)(141,289)(142,290)(143,292)(144,291)(145,285)(146,286)(147,288)(148,287)(149,281)(150,282)(151,284)(152,283)(153,277)(154,278)(155,280)(156,279)(157,273)(158,274)(159,276)(160,275)(161,269)(162,270)(163,272)(164,271)(165,265)(166,266)(167,268)(168,267)(169,261)(170,262)(171,264)(172,263)(173,257)(174,258)(175,260)(176,259)(177,253)(178,254)(179,256)(180,255)(181,249)(182,250)(183,252)(184,251)(185,245)(186,246)(187,248)(188,247)(189,241)(190,242)(191,244)(192,243)(193,237)(194,238)(195,240)(196,239)(197,233)(198,234)(199,236)(200,235)(201,229)(202,230)(203,232)(204,231)(205,225)(206,226)(207,228)(208,227)(209,221)(210,222)(211,224)(212,223)(213,217)(214,218)(215,220)(216,219)(327,328)(329,333)(330,334)(331,336)(332,335)(337,357)(338,358)(339,360)(340,359)(341,353)(342,354)(343,356)(344,355)(345,349)(346,350)(347,352)(348,351)(361,429)(362,430)(363,432)(364,431)(365,425)(366,426)(367,428)(368,427)(369,421)(370,422)(371,424)(372,423)(373,417)(374,418)(375,420)(376,419)(377,413)(378,414)(379,416)(380,415)(381,409)(382,410)(383,412)(384,411)(385,405)(386,406)(387,408)(388,407)(389,401)(390,402)(391,404)(392,403)(393,397)(394,398)(395,400)(396,399)(433,645)(434,646)(435,648)(436,647)(437,641)(438,642)(439,644)(440,643)(441,637)(442,638)(443,640)(444,639)(445,633)(446,634)(447,636)(448,635)(449,629)(450,630)(451,632)(452,631)(453,625)(454,626)(455,628)(456,627)(457,621)(458,622)(459,624)(460,623)(461,617)(462,618)(463,620)(464,619)(465,613)(466,614)(467,616)(468,615)(469,609)(470,610)(471,612)(472,611)(473,605)(474,606)(475,608)(476,607)(477,601)(478,602)(479,604)(480,603)(481,597)(482,598)(483,600)(484,599)(485,593)(486,594)(487,596)(488,595)(489,589)(490,590)(491,592)(492,591)(493,585)(494,586)(495,588)(496,587)(497,581)(498,582)(499,584)(500,583)(501,577)(502,578)(503,580)(504,579)(505,573)(506,574)(507,576)(508,575)(509,569)(510,570)(511,572)(512,571)(513,565)(514,566)(515,568)(516,567)(517,561)(518,562)(519,564)(520,563)(521,557)(522,558)(523,560)(524,559)(525,553)(526,554)(527,556)(528,555)(529,549)(530,550)(531,552)(532,551)(533,545)(534,546)(535,548)(536,547)(537,541)(538,542)(539,544)(540,543);
s1 := Sym(648)!(  1,433)(  2,436)(  3,435)(  4,434)(  5,441)(  6,444)(  7,443)(  8,442)(  9,437)( 10,440)( 11,439)( 12,438)( 13,465)( 14,468)( 15,467)( 16,466)( 17,461)( 18,464)( 19,463)( 20,462)( 21,457)( 22,460)( 23,459)( 24,458)( 25,453)( 26,456)( 27,455)( 28,454)( 29,449)( 30,452)( 31,451)( 32,450)( 33,445)( 34,448)( 35,447)( 36,446)( 37,537)( 38,540)( 39,539)( 40,538)( 41,533)( 42,536)( 43,535)( 44,534)( 45,529)( 46,532)( 47,531)( 48,530)( 49,525)( 50,528)( 51,527)( 52,526)( 53,521)( 54,524)( 55,523)( 56,522)( 57,517)( 58,520)( 59,519)( 60,518)( 61,513)( 62,516)( 63,515)( 64,514)( 65,509)( 66,512)( 67,511)( 68,510)( 69,505)( 70,508)( 71,507)( 72,506)( 73,501)( 74,504)( 75,503)( 76,502)( 77,497)( 78,500)( 79,499)( 80,498)( 81,493)( 82,496)( 83,495)( 84,494)( 85,489)( 86,492)( 87,491)( 88,490)( 89,485)( 90,488)( 91,487)( 92,486)( 93,481)( 94,484)( 95,483)( 96,482)( 97,477)( 98,480)( 99,479)(100,478)(101,473)(102,476)(103,475)(104,474)(105,469)(106,472)(107,471)(108,470)(109,325)(110,328)(111,327)(112,326)(113,333)(114,336)(115,335)(116,334)(117,329)(118,332)(119,331)(120,330)(121,357)(122,360)(123,359)(124,358)(125,353)(126,356)(127,355)(128,354)(129,349)(130,352)(131,351)(132,350)(133,345)(134,348)(135,347)(136,346)(137,341)(138,344)(139,343)(140,342)(141,337)(142,340)(143,339)(144,338)(145,429)(146,432)(147,431)(148,430)(149,425)(150,428)(151,427)(152,426)(153,421)(154,424)(155,423)(156,422)(157,417)(158,420)(159,419)(160,418)(161,413)(162,416)(163,415)(164,414)(165,409)(166,412)(167,411)(168,410)(169,405)(170,408)(171,407)(172,406)(173,401)(174,404)(175,403)(176,402)(177,397)(178,400)(179,399)(180,398)(181,393)(182,396)(183,395)(184,394)(185,389)(186,392)(187,391)(188,390)(189,385)(190,388)(191,387)(192,386)(193,381)(194,384)(195,383)(196,382)(197,377)(198,380)(199,379)(200,378)(201,373)(202,376)(203,375)(204,374)(205,369)(206,372)(207,371)(208,370)(209,365)(210,368)(211,367)(212,366)(213,361)(214,364)(215,363)(216,362)(217,645)(218,648)(219,647)(220,646)(221,641)(222,644)(223,643)(224,642)(225,637)(226,640)(227,639)(228,638)(229,633)(230,636)(231,635)(232,634)(233,629)(234,632)(235,631)(236,630)(237,625)(238,628)(239,627)(240,626)(241,621)(242,624)(243,623)(244,622)(245,617)(246,620)(247,619)(248,618)(249,613)(250,616)(251,615)(252,614)(253,609)(254,612)(255,611)(256,610)(257,605)(258,608)(259,607)(260,606)(261,601)(262,604)(263,603)(264,602)(265,597)(266,600)(267,599)(268,598)(269,593)(270,596)(271,595)(272,594)(273,589)(274,592)(275,591)(276,590)(277,585)(278,588)(279,587)(280,586)(281,581)(282,584)(283,583)(284,582)(285,577)(286,580)(287,579)(288,578)(289,573)(290,576)(291,575)(292,574)(293,569)(294,572)(295,571)(296,570)(297,565)(298,568)(299,567)(300,566)(301,561)(302,564)(303,563)(304,562)(305,557)(306,560)(307,559)(308,558)(309,553)(310,556)(311,555)(312,554)(313,549)(314,552)(315,551)(316,550)(317,545)(318,548)(319,547)(320,546)(321,541)(322,544)(323,543)(324,542);
s2 := Sym(648)!(  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);
poly := sub<Sym(648)|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 >; 
 

Twisty Puzzle