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# Polytope of Type {6,4}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {6,4}*672a
if this polytope has a name.
Group : SmallGroup(672,1254)
Rank : 3
Schlafli Type : {6,4}
Number of vertices, edges, etc : 84, 168, 56
Order of s0s1s2 : 8
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Skewing Operation
Facet Of :
{6,4,2} of size 1344
Vertex Figure Of :
{2,6,4} of size 1344
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {6,4}*336
Covers (Minimal Covers in Boldface) :
2-fold covers : {6,4}*1344
Permutation Representation (GAP) :
```s0 := (3,7)(4,8)(5,6);;
s1 := (1,3)(2,5)(4,8)(6,7);;
s2 := ( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);;
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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(10)!(3,7)(4,8)(5,6);
s1 := Sym(10)!(1,3)(2,5)(4,8)(6,7);
s2 := Sym(10)!( 1, 2)( 3, 4)( 5, 6)( 7, 8)( 9,10);
poly := sub<Sym(10)|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,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s2*s1*s2*s1*s0*s1*s0*s2*s1*s2*s1*s0*s1*s2*s0*s1*s2*s1 >;

```
References : None.
to this polytope