Polytope of Type {8,6}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,6}*384c
if this polytope has a name.
Group : SmallGroup(384,5602)
Rank : 3
Schlafli Type : {8,6}
Number of vertices, edges, etc : 32, 96, 24
Order of s₀s₁s₂ : 6
Order of s₀s₁s₂s₁ : 4
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Non-Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   {8,6,2} of size 768
Vertex Figure Of :
   {2,8,6} of size 768
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {4,6}*192a
   8-fold quotients : {4,6}*48c
   16-fold quotients : {4,3}*24
Covers (Minimal Covers in Boldface) :
   2-fold covers : {8,12}*768f, {8,12}*768h, {8,6}*768m
   3-fold covers : {8,18}*1152c
   5-fold covers : {8,30}*1920c
Permutation Representation (GAP) :

s0 := (1,5)(2,6)(3,7)(4,8);;
s1 := (3,6)(4,5)(7,8);;
s2 := (3,8)(4,7);;
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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1 ];;
poly := F / rels;;

Permutation Representation (Magma) :

s0 := Sym(8)!(1,5)(2,6)(3,7)(4,8);
s1 := Sym(8)!(3,6)(4,5)(7,8);
s2 := Sym(8)!(3,8)(4,7);
poly := sub<Sym(8)|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, 
s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1, 
s2*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0*s1*s2*s1 >;

References : None.
to this polytope