Polytope of Type {12,60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,60}*1920c
if this polytope has a name.
Group : SmallGroup(1920,238871)
Rank : 3
Schlafli Type : {12,60}
Number of vertices, edges, etc : 16, 480, 80
Order of s₀s₁s₂ : 20
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,60}*960a, {12,30}*960b
   4-fold quotients : {6,30}*480
   5-fold quotients : {12,12}*384a
   8-fold quotients : {6,15}*240
   10-fold quotients : {6,12}*192a, {12,6}*192a
   12-fold quotients : {4,20}*160
   20-fold quotients : {6,6}*96
   24-fold quotients : {2,20}*80, {4,10}*80
   40-fold quotients : {3,6}*48, {6,3}*48
   48-fold quotients : {2,10}*40
   60-fold quotients : {4,4}*32
   80-fold quotients : {3,3}*24
   96-fold quotients : {2,5}*20
   120-fold quotients : {2,4}*16, {4,2}*16
   240-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope