Questions?
See the FAQ
or other info.

# Polytope of Type {3,7}

Atlas Canonical Name : {3,7}*336
Also Known As : {3,7}8if this polytope has another name.
Group : SmallGroup(336,208)
Rank : 3
Schlafli Type : {3,7}
Number of vertices, edges, etc : 24, 84, 56
Order of s0s1s2 : 8
Order of s0s1s2s1 : 7
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{3,7,2} of size 672
Vertex Figure Of :
{2,3,7} of size 672
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {3,14}*672, {6,7}*672a
3-fold covers : {3,21}*1008
4-fold covers : {3,28}*1344, {12,7}*1344, {6,14}*1344b
Permutation Representation (GAP) :
```s0 := (3,7)(4,8)(5,6);;
s1 := (1,3)(2,8)(5,6);;
s2 := (1,2)(4,6)(5,8);;
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, s0*s1*s0*s1*s0*s1,
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*s0*s1*s2*s0*s1 ];;
poly := F / rels;;

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

```
References : None.
to this polytope