Polytope of Type {8,9}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle