Polytope of Type {66,14}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {66,14}*1848
Also Known As : {66,14|2}. if this polytope has another name.
Group : SmallGroup(1848,149)
Rank : 3
Schlafli Type : {66,14}
Number of vertices, edges, etc : 66, 462, 14
Order of s0s1s2 : 462
Order of s0s1s2s1 : 2
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {22,14}*616
   7-fold quotients : {66,2}*264
   11-fold quotients : {6,14}*168
   14-fold quotients : {33,2}*132
   21-fold quotients : {22,2}*88
   33-fold quotients : {2,14}*56
   42-fold quotients : {11,2}*44
   66-fold quotients : {2,7}*28
   77-fold quotients : {6,2}*24
   154-fold quotients : {3,2}*12
   231-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   None.

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

Twisty Puzzle