Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*1344a
if this polytope has a name.
Group : SmallGroup(1344,11291)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 112, 336, 84
Order of s₀s₁s₂ : 16
Order of s₀s₁s₂s₁ : 16
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 : {4,6}*672c
   4-fold quotients : {4,6}*336
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Permutation Representation (GAP) :

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

Permutation Representation (Magma) :

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

References : None.
to this polytope