Polytope of Type {4,138}

Play with this polytope as a twisty puzzle

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