Polytope of Type {60}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60}*120
Also Known As : 60-gon, {60}. if this polytope has another name.
Group : SmallGroup(120,28)
Rank : 2
Schlafli Type : {60}
Number of vertices, edges, etc : 60, 60
Order of s₀s₁ : 60
Special Properties :
   Universal
   Spherical
   Locally Spherical
   Orientable
   Self-Dual
Related Polytopes :
   Facet
   Vertex Figure
   Dual
Facet Of :
   {60,2} of size 240
   {60,4} of size 480
   {60,4} of size 480
   {60,4} of size 480
   {60,6} of size 720
   {60,6} of size 720
   {60,6} of size 720
   {60,6} of size 720
   {60,4} of size 960
   {60,8} of size 960
   {60,8} of size 960
   {60,6} of size 960
   {60,6} of size 960
   {60,4} of size 960
   {60,4} of size 960
   {60,6} of size 1080
   {60,6} of size 1080
   {60,6} of size 1080
   {60,10} of size 1200
   {60,10} of size 1200
   {60,10} of size 1200
   {60,12} of size 1440
   {60,12} of size 1440
   {60,12} of size 1440
   {60,6} of size 1440
   {60,6} of size 1440
   {60,10} of size 1440
   {60,10} of size 1440
   {60,3} of size 1440
   {60,4} of size 1440
   {60,6} of size 1440
   {60,6} of size 1440
   {60,14} of size 1680
   {60,8} of size 1920
   {60,16} of size 1920
   {60,16} of size 1920
   {60,4} of size 1920
   {60,8} of size 1920
   {60,4} of size 1920
   {60,4} of size 1920
   {60,8} of size 1920
   {60,8} of size 1920
   {60,12} of size 1920
   {60,12} of size 1920
   {60,6} of size 1920
   {60,12} of size 1920
   {60,12} of size 1920
   {60,4} of size 1920
   {60,8} of size 1920
   {60,8} of size 1920
   {60,8} of size 1920
   {60,8} of size 1920
   {60,4} of size 1920
   {60,4} of size 1920
   {60,4} of size 1920
   {60,4} of size 1920
   {60,4} of size 1920
Vertex Figure Of :
   {2,60} of size 240
   {4,60} of size 480
   {4,60} of size 480
   {4,60} of size 480
   {6,60} of size 720
   {6,60} of size 720
   {6,60} of size 720
   {6,60} of size 720
   {4,60} of size 960
   {8,60} of size 960
   {8,60} of size 960
   {6,60} of size 960
   {6,60} of size 960
   {4,60} of size 960
   {4,60} of size 960
   {6,60} of size 1080
   {6,60} of size 1080
   {6,60} of size 1080
   {10,60} of size 1200
   {10,60} of size 1200
   {10,60} of size 1200
   {12,60} of size 1440
   {12,60} of size 1440
   {12,60} of size 1440
   {6,60} of size 1440
   {6,60} of size 1440
   {10,60} of size 1440
   {10,60} of size 1440
   {3,60} of size 1440
   {4,60} of size 1440
   {6,60} of size 1440
   {6,60} of size 1440
   {14,60} of size 1680
   {8,60} of size 1920
   {16,60} of size 1920
   {16,60} of size 1920
   {4,60} of size 1920
   {8,60} of size 1920
   {4,60} of size 1920
   {4,60} of size 1920
   {8,60} of size 1920
   {8,60} of size 1920
   {12,60} of size 1920
   {12,60} of size 1920
   {6,60} of size 1920
   {12,60} of size 1920
   {12,60} of size 1920
   {4,60} of size 1920
   {8,60} of size 1920
   {8,60} of size 1920
   {8,60} of size 1920
   {8,60} of size 1920
   {4,60} of size 1920
   {4,60} of size 1920
   {4,60} of size 1920
   {4,60} of size 1920
   {4,60} of size 1920
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {30}*60
   3-fold quotients : {20}*40
   4-fold quotients : {15}*30
   5-fold quotients : {12}*24
   6-fold quotients : {10}*20
   10-fold quotients : {6}*12
   12-fold quotients : {5}*10
   15-fold quotients : {4}*8
   20-fold quotients : {3}*6
   30-fold quotients : {2}*4
Covers (Minimal Covers in Boldface) :
   2-fold covers : {120}*240
   3-fold covers : {180}*360
   4-fold covers : {240}*480
   5-fold covers : {300}*600
   6-fold covers : {360}*720
   7-fold covers : {420}*840
   8-fold covers : {480}*960
   9-fold covers : {540}*1080
   10-fold covers : {600}*1200
   11-fold covers : {660}*1320
   12-fold covers : {720}*1440
   13-fold covers : {780}*1560
   14-fold covers : {840}*1680
   15-fold covers : {900}*1800
   16-fold covers : {960}*1920
Permutation Representation (GAP) :

s0 := ( 2, 3)( 4, 5)( 6, 7)( 9,14)(10,13)(11,16)(12,15)(17,20)(18,19)(21,22)
(23,24)(25,26)(27,36)(28,35)(29,34)(30,33)(31,38)(32,37)(39,42)(40,41)(43,46)
(44,45)(47,48)(49,56)(50,55)(51,54)(52,53)(57,60)(58,59);;
s1 := ( 1,27)( 2,17)( 3,43)( 4,11)( 5,29)( 6, 9)( 7,49)( 8,33)(10,19)(12,39)
(13,25)(14,45)(15,23)(16,57)(18,31)(20,51)(21,28)(22,50)(24,35)(26,53)(30,41)
(32,40)(34,47)(36,59)(37,44)(38,58)(42,52)(46,55)(48,54)(56,60);;
poly := Group([s0,s1]);;

Finitely Presented Group Representation (GAP) :

F := FreeGroup("s0","s1");;
s0 := F.1;;  s1 := F.2;;  
rels := [ s0*s0, s1*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(60)!( 2, 3)( 4, 5)( 6, 7)( 9,14)(10,13)(11,16)(12,15)(17,20)(18,19)
(21,22)(23,24)(25,26)(27,36)(28,35)(29,34)(30,33)(31,38)(32,37)(39,42)(40,41)
(43,46)(44,45)(47,48)(49,56)(50,55)(51,54)(52,53)(57,60)(58,59);
s1 := Sym(60)!( 1,27)( 2,17)( 3,43)( 4,11)( 5,29)( 6, 9)( 7,49)( 8,33)(10,19)
(12,39)(13,25)(14,45)(15,23)(16,57)(18,31)(20,51)(21,28)(22,50)(24,35)(26,53)
(30,41)(32,40)(34,47)(36,59)(37,44)(38,58)(42,52)(46,55)(48,54)(56,60);
poly := sub<Sym(60)|s0,s1>;

Finitely Presented Group Representation (Magma) :

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