Polytope of Type {60,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {60,6}*720d
if this polytope has a name.
Group : SmallGroup(720,794)
Rank : 3
Schlafli Type : {60,6}
Number of vertices, edges, etc : 60, 180, 6
Order of s₀s₁s₂ : 15
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
   Flat
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {60,6,2} of size 1440
Vertex Figure Of :
   {2,60,6} of size 1440
Quotients (Maximal Quotients in Boldface) :
   3-fold quotients : {20,6}*240b
   5-fold quotients : {12,6}*144d
   15-fold quotients : {4,6}*48b
   30-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {60,6}*1440d
Permutation Representation (GAP) :

s0 := ( 1, 3)( 2, 4)( 5,19)( 6,20)( 7,17)( 8,18)( 9,15)(10,16)(11,13)(12,14)
(21,43)(22,44)(23,41)(24,42)(25,59)(26,60)(27,57)(28,58)(29,55)(30,56)(31,53)
(32,54)(33,51)(34,52)(35,49)(36,50)(37,47)(38,48)(39,45)(40,46);;
s1 := ( 1,25)( 2,27)( 3,26)( 4,28)( 5,21)( 6,23)( 7,22)( 8,24)( 9,37)(10,39)
(11,38)(12,40)(13,33)(14,35)(15,34)(16,36)(17,29)(18,31)(19,30)(20,32)(41,45)
(42,47)(43,46)(44,48)(49,57)(50,59)(51,58)(52,60)(54,55);;
s2 := ( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36)(38,40)
(42,44)(46,48)(50,52)(54,56)(58,60);;
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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(60)!( 1, 3)( 2, 4)( 5,19)( 6,20)( 7,17)( 8,18)( 9,15)(10,16)(11,13)
(12,14)(21,43)(22,44)(23,41)(24,42)(25,59)(26,60)(27,57)(28,58)(29,55)(30,56)
(31,53)(32,54)(33,51)(34,52)(35,49)(36,50)(37,47)(38,48)(39,45)(40,46);
s1 := Sym(60)!( 1,25)( 2,27)( 3,26)( 4,28)( 5,21)( 6,23)( 7,22)( 8,24)( 9,37)
(10,39)(11,38)(12,40)(13,33)(14,35)(15,34)(16,36)(17,29)(18,31)(19,30)(20,32)
(41,45)(42,47)(43,46)(44,48)(49,57)(50,59)(51,58)(52,60)(54,55);
s2 := Sym(60)!( 2, 4)( 6, 8)(10,12)(14,16)(18,20)(22,24)(26,28)(30,32)(34,36)
(38,40)(42,44)(46,48)(50,52)(54,56)(58,60);
poly := sub<Sym(60)|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, s1*s2*s1*s2*s1*s2*s1*s2*s1*s2*s1*s2, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1, 
s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s0*s1*s2*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0 >;

References : None.
to this polytope