Polytope of Type {36,8}

Play with this polytope as a twisty puzzle

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

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

Twisty Puzzle