Polytope of Type {5,12}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {5,12}*1920e
if this polytope has a name.
Group : SmallGroup(1920,241004)
Rank : 3
Schlafli Type : {5,12}
Number of vertices, edges, etc : 80, 480, 192
Order of s₀s₁s₂ : 10
Order of s₀s₁s₂s₁ : 10
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-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 : {5,6}*960
   32-fold quotients : {5,3}*60
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

s0 := ( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)(20,31)
(21,28)(22,27)(23,32)(24,26);;
s1 := ( 1, 3)( 2,27)( 4,21)( 5,17)( 6,14)( 7,15)( 8,16)(10,29)(11,32)(12,23)
(13,19)(18,31)(22,30)(24,26);;
s2 := ( 3,15)( 4, 5)( 7,30)( 8, 9)(11,31)(12,24)(13,28)(14,32)(16,20)(17,26)
(18,22)(19,23)(21,25)(27,29);;
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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(32)!( 3, 4)( 5,15)( 7, 8)( 9,30)(11,16)(12,17)(13,25)(14,19)(18,29)
(20,31)(21,28)(22,27)(23,32)(24,26);
s1 := Sym(32)!( 1, 3)( 2,27)( 4,21)( 5,17)( 6,14)( 7,15)( 8,16)(10,29)(11,32)
(12,23)(13,19)(18,31)(22,30)(24,26);
s2 := Sym(32)!( 3,15)( 4, 5)( 7,30)( 8, 9)(11,31)(12,24)(13,28)(14,32)(16,20)
(17,26)(18,22)(19,23)(21,25)(27,29);
poly := sub<Sym(32)|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*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s2*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2, 
s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1*s0*s1*s2*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1 >;

References : None.
to this polytope