Questions?
See the FAQ
or other info.

# Polytope of Type {8,6}

Atlas Canonical Name : {8,6}*384b
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}*768e, {8,12}*768g, {8,6}*768b, {8,6}*768c, {8,12}*768i, {8,12}*768j, {8,6}*768m
3-fold covers : {8,18}*1152b
5-fold covers : {8,30}*1920b
Permutation Representation (GAP) :
```s0 := (1,5)(2,6)(3,7)(4,8);;
s1 := (3,6)(4,5)(7,8);;
s2 := (3,7)(4,8);;
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*s2*s1*s2*s0*s1*s2*s1*s2*s0*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 ];;
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)!(3,7)(4,8);
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*s2*s1*s2*s0*s1*s2*s1*s2*s0*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 >;

```
References : None.
to this polytope