Polytope of Type {12,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,6}*1152i
if this polytope has a name.
Group : SmallGroup(1152,157478)
Rank : 3
Schlafli Type : {12,6}
Number of vertices, edges, etc : 96, 288, 48
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {6,6}*576e
   32-fold quotients : {3,6}*36
   96-fold quotients : {3,2}*12
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope