Polytope of Type {6,8}

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

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

Permutation Representation (Magma) :

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

References : None.
to this polytope