Polytope of Type {6,129}

Play with this polytope as a twisty puzzle

s0 := ( 44, 87)( 45, 88)( 46, 89)( 47, 90)( 48, 91)( 49, 92)( 50, 93)( 51, 94)( 52, 95)( 53, 96)( 54, 97)( 55, 98)( 56, 99)( 57,100)( 58,101)( 59,102)( 60,103)( 61,104)( 62,105)( 63,106)( 64,107)( 65,108)( 66,109)( 67,110)( 68,111)( 69,112)( 70,113)( 71,114)( 72,115)( 73,116)( 74,117)( 75,118)( 76,119)( 77,120)( 78,121)( 79,122)( 80,123)( 81,124)( 82,125)( 83,126)( 84,127)( 85,128)( 86,129)(173,216)(174,217)(175,218)(176,219)(177,220)(178,221)(179,222)(180,223)(181,224)(182,225)(183,226)(184,227)(185,228)(186,229)(187,230)(188,231)(189,232)(190,233)(191,234)(192,235)(193,236)(194,237)(195,238)(196,239)(197,240)(198,241)(199,242)(200,243)(201,244)(202,245)(203,246)(204,247)(205,248)(206,249)(207,250)(208,251)(209,252)(210,253)(211,254)(212,255)(213,256)(214,257)(215,258)(302,345)(303,346)(304,347)(305,348)(306,349)(307,350)(308,351)(309,352)(310,353)(311,354)(312,355)(313,356)(314,357)(315,358)(316,359)(317,360)(318,361)(319,362)(320,363)(321,364)(322,365)(323,366)(324,367)(325,368)(326,369)(327,370)(328,371)(329,372)(330,373)(331,374)(332,375)(333,376)(334,377)(335,378)(336,379)(337,380)(338,381)(339,382)(340,383)(341,384)(342,385)(343,386)(344,387);;
s1 := (  1, 44)(  2, 86)(  3, 85)(  4, 84)(  5, 83)(  6, 82)(  7, 81)(  8, 80)(  9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)( 16, 72)( 17, 71)( 18, 70)( 19, 69)( 20, 68)( 21, 67)( 22, 66)( 23, 65)( 24, 64)( 25, 63)( 26, 62)( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)( 33, 55)( 34, 54)( 35, 53)( 36, 52)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)( 88,129)( 89,128)( 90,127)( 91,126)( 92,125)( 93,124)( 94,123)( 95,122)( 96,121)( 97,120)( 98,119)( 99,118)(100,117)(101,116)(102,115)(103,114)(104,113)(105,112)(106,111)(107,110)(108,109)(130,302)(131,344)(132,343)(133,342)(134,341)(135,340)(136,339)(137,338)(138,337)(139,336)(140,335)(141,334)(142,333)(143,332)(144,331)(145,330)(146,329)(147,328)(148,327)(149,326)(150,325)(151,324)(152,323)(153,322)(154,321)(155,320)(156,319)(157,318)(158,317)(159,316)(160,315)(161,314)(162,313)(163,312)(164,311)(165,310)(166,309)(167,308)(168,307)(169,306)(170,305)(171,304)(172,303)(173,259)(174,301)(175,300)(176,299)(177,298)(178,297)(179,296)(180,295)(181,294)(182,293)(183,292)(184,291)(185,290)(186,289)(187,288)(188,287)(189,286)(190,285)(191,284)(192,283)(193,282)(194,281)(195,280)(196,279)(197,278)(198,277)(199,276)(200,275)(201,274)(202,273)(203,272)(204,271)(205,270)(206,269)(207,268)(208,267)(209,266)(210,265)(211,264)(212,263)(213,262)(214,261)(215,260)(216,345)(217,387)(218,386)(219,385)(220,384)(221,383)(222,382)(223,381)(224,380)(225,379)(226,378)(227,377)(228,376)(229,375)(230,374)(231,373)(232,372)(233,371)(234,370)(235,369)(236,368)(237,367)(238,366)(239,365)(240,364)(241,363)(242,362)(243,361)(244,360)(245,359)(246,358)(247,357)(248,356)(249,355)(250,354)(251,353)(252,352)(253,351)(254,350)(255,349)(256,348)(257,347)(258,346);;
s2 := (  1,131)(  2,130)(  3,172)(  4,171)(  5,170)(  6,169)(  7,168)(  8,167)(  9,166)( 10,165)( 11,164)( 12,163)( 13,162)( 14,161)( 15,160)( 16,159)( 17,158)( 18,157)( 19,156)( 20,155)( 21,154)( 22,153)( 23,152)( 24,151)( 25,150)( 26,149)( 27,148)( 28,147)( 29,146)( 30,145)( 31,144)( 32,143)( 33,142)( 34,141)( 35,140)( 36,139)( 37,138)( 38,137)( 39,136)( 40,135)( 41,134)( 42,133)( 43,132)( 44,217)( 45,216)( 46,258)( 47,257)( 48,256)( 49,255)( 50,254)( 51,253)( 52,252)( 53,251)( 54,250)( 55,249)( 56,248)( 57,247)( 58,246)( 59,245)( 60,244)( 61,243)( 62,242)( 63,241)( 64,240)( 65,239)( 66,238)( 67,237)( 68,236)( 69,235)( 70,234)( 71,233)( 72,232)( 73,231)( 74,230)( 75,229)( 76,228)( 77,227)( 78,226)( 79,225)( 80,224)( 81,223)( 82,222)( 83,221)( 84,220)( 85,219)( 86,218)( 87,174)( 88,173)( 89,215)( 90,214)( 91,213)( 92,212)( 93,211)( 94,210)( 95,209)( 96,208)( 97,207)( 98,206)( 99,205)(100,204)(101,203)(102,202)(103,201)(104,200)(105,199)(106,198)(107,197)(108,196)(109,195)(110,194)(111,193)(112,192)(113,191)(114,190)(115,189)(116,188)(117,187)(118,186)(119,185)(120,184)(121,183)(122,182)(123,181)(124,180)(125,179)(126,178)(127,177)(128,176)(129,175)(259,260)(261,301)(262,300)(263,299)(264,298)(265,297)(266,296)(267,295)(268,294)(269,293)(270,292)(271,291)(272,290)(273,289)(274,288)(275,287)(276,286)(277,285)(278,284)(279,283)(280,282)(302,346)(303,345)(304,387)(305,386)(306,385)(307,384)(308,383)(309,382)(310,381)(311,380)(312,379)(313,378)(314,377)(315,376)(316,375)(317,374)(318,373)(319,372)(320,371)(321,370)(322,369)(323,368)(324,367)(325,366)(326,365)(327,364)(328,363)(329,362)(330,361)(331,360)(332,359)(333,358)(334,357)(335,356)(336,355)(337,354)(338,353)(339,352)(340,351)(341,350)(342,349)(343,348)(344,347);;
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*s0*s1*s0*s1*s2*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*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*s1*s2 ];;
poly := F / rels;;
 

s0 := Sym(387)!( 44, 87)( 45, 88)( 46, 89)( 47, 90)( 48, 91)( 49, 92)( 50, 93)( 51, 94)( 52, 95)( 53, 96)( 54, 97)( 55, 98)( 56, 99)( 57,100)( 58,101)( 59,102)( 60,103)( 61,104)( 62,105)( 63,106)( 64,107)( 65,108)( 66,109)( 67,110)( 68,111)( 69,112)( 70,113)( 71,114)( 72,115)( 73,116)( 74,117)( 75,118)( 76,119)( 77,120)( 78,121)( 79,122)( 80,123)( 81,124)( 82,125)( 83,126)( 84,127)( 85,128)( 86,129)(173,216)(174,217)(175,218)(176,219)(177,220)(178,221)(179,222)(180,223)(181,224)(182,225)(183,226)(184,227)(185,228)(186,229)(187,230)(188,231)(189,232)(190,233)(191,234)(192,235)(193,236)(194,237)(195,238)(196,239)(197,240)(198,241)(199,242)(200,243)(201,244)(202,245)(203,246)(204,247)(205,248)(206,249)(207,250)(208,251)(209,252)(210,253)(211,254)(212,255)(213,256)(214,257)(215,258)(302,345)(303,346)(304,347)(305,348)(306,349)(307,350)(308,351)(309,352)(310,353)(311,354)(312,355)(313,356)(314,357)(315,358)(316,359)(317,360)(318,361)(319,362)(320,363)(321,364)(322,365)(323,366)(324,367)(325,368)(326,369)(327,370)(328,371)(329,372)(330,373)(331,374)(332,375)(333,376)(334,377)(335,378)(336,379)(337,380)(338,381)(339,382)(340,383)(341,384)(342,385)(343,386)(344,387);
s1 := Sym(387)!(  1, 44)(  2, 86)(  3, 85)(  4, 84)(  5, 83)(  6, 82)(  7, 81)(  8, 80)(  9, 79)( 10, 78)( 11, 77)( 12, 76)( 13, 75)( 14, 74)( 15, 73)( 16, 72)( 17, 71)( 18, 70)( 19, 69)( 20, 68)( 21, 67)( 22, 66)( 23, 65)( 24, 64)( 25, 63)( 26, 62)( 27, 61)( 28, 60)( 29, 59)( 30, 58)( 31, 57)( 32, 56)( 33, 55)( 34, 54)( 35, 53)( 36, 52)( 37, 51)( 38, 50)( 39, 49)( 40, 48)( 41, 47)( 42, 46)( 43, 45)( 88,129)( 89,128)( 90,127)( 91,126)( 92,125)( 93,124)( 94,123)( 95,122)( 96,121)( 97,120)( 98,119)( 99,118)(100,117)(101,116)(102,115)(103,114)(104,113)(105,112)(106,111)(107,110)(108,109)(130,302)(131,344)(132,343)(133,342)(134,341)(135,340)(136,339)(137,338)(138,337)(139,336)(140,335)(141,334)(142,333)(143,332)(144,331)(145,330)(146,329)(147,328)(148,327)(149,326)(150,325)(151,324)(152,323)(153,322)(154,321)(155,320)(156,319)(157,318)(158,317)(159,316)(160,315)(161,314)(162,313)(163,312)(164,311)(165,310)(166,309)(167,308)(168,307)(169,306)(170,305)(171,304)(172,303)(173,259)(174,301)(175,300)(176,299)(177,298)(178,297)(179,296)(180,295)(181,294)(182,293)(183,292)(184,291)(185,290)(186,289)(187,288)(188,287)(189,286)(190,285)(191,284)(192,283)(193,282)(194,281)(195,280)(196,279)(197,278)(198,277)(199,276)(200,275)(201,274)(202,273)(203,272)(204,271)(205,270)(206,269)(207,268)(208,267)(209,266)(210,265)(211,264)(212,263)(213,262)(214,261)(215,260)(216,345)(217,387)(218,386)(219,385)(220,384)(221,383)(222,382)(223,381)(224,380)(225,379)(226,378)(227,377)(228,376)(229,375)(230,374)(231,373)(232,372)(233,371)(234,370)(235,369)(236,368)(237,367)(238,366)(239,365)(240,364)(241,363)(242,362)(243,361)(244,360)(245,359)(246,358)(247,357)(248,356)(249,355)(250,354)(251,353)(252,352)(253,351)(254,350)(255,349)(256,348)(257,347)(258,346);
s2 := Sym(387)!(  1,131)(  2,130)(  3,172)(  4,171)(  5,170)(  6,169)(  7,168)(  8,167)(  9,166)( 10,165)( 11,164)( 12,163)( 13,162)( 14,161)( 15,160)( 16,159)( 17,158)( 18,157)( 19,156)( 20,155)( 21,154)( 22,153)( 23,152)( 24,151)( 25,150)( 26,149)( 27,148)( 28,147)( 29,146)( 30,145)( 31,144)( 32,143)( 33,142)( 34,141)( 35,140)( 36,139)( 37,138)( 38,137)( 39,136)( 40,135)( 41,134)( 42,133)( 43,132)( 44,217)( 45,216)( 46,258)( 47,257)( 48,256)( 49,255)( 50,254)( 51,253)( 52,252)( 53,251)( 54,250)( 55,249)( 56,248)( 57,247)( 58,246)( 59,245)( 60,244)( 61,243)( 62,242)( 63,241)( 64,240)( 65,239)( 66,238)( 67,237)( 68,236)( 69,235)( 70,234)( 71,233)( 72,232)( 73,231)( 74,230)( 75,229)( 76,228)( 77,227)( 78,226)( 79,225)( 80,224)( 81,223)( 82,222)( 83,221)( 84,220)( 85,219)( 86,218)( 87,174)( 88,173)( 89,215)( 90,214)( 91,213)( 92,212)( 93,211)( 94,210)( 95,209)( 96,208)( 97,207)( 98,206)( 99,205)(100,204)(101,203)(102,202)(103,201)(104,200)(105,199)(106,198)(107,197)(108,196)(109,195)(110,194)(111,193)(112,192)(113,191)(114,190)(115,189)(116,188)(117,187)(118,186)(119,185)(120,184)(121,183)(122,182)(123,181)(124,180)(125,179)(126,178)(127,177)(128,176)(129,175)(259,260)(261,301)(262,300)(263,299)(264,298)(265,297)(266,296)(267,295)(268,294)(269,293)(270,292)(271,291)(272,290)(273,289)(274,288)(275,287)(276,286)(277,285)(278,284)(279,283)(280,282)(302,346)(303,345)(304,387)(305,386)(306,385)(307,384)(308,383)(309,382)(310,381)(311,380)(312,379)(313,378)(314,377)(315,376)(316,375)(317,374)(318,373)(319,372)(320,371)(321,370)(322,369)(323,368)(324,367)(325,366)(326,365)(327,364)(328,363)(329,362)(330,361)(331,360)(332,359)(333,358)(334,357)(335,356)(336,355)(337,354)(338,353)(339,352)(340,351)(341,350)(342,349)(343,348)(344,347);
poly := sub<Sym(387)|s0,s1,s2>;
 

poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s2*s0*s1*s0*s1*s2*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*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*s1*s2 >; 
 

Twisty Puzzle