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# Polytope of Type {7,8}

Atlas Canonical Name : {7,8}*336a
if this polytope has a name.
Group : SmallGroup(336,208)
Rank : 3
Schlafli Type : {7,8}
Number of vertices, edges, etc : 21, 84, 24
Order of s0s1s2 : 4
Order of s0s1s2s1 : 8
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Petrial
Facet Of :
{7,8,2} of size 672
Vertex Figure Of :
{2,7,8} of size 672
Quotients (Maximal Quotients in Boldface) :
No Regular Quotients.
Covers (Minimal Covers in Boldface) :
2-fold covers : {7,8}*672a, {14,8}*672a, {14,8}*672b
3-fold covers : {21,8}*1008b
4-fold covers : {28,8}*1344a, {28,8}*1344b, {7,16}*1344b, {14,8}*1344a
5-fold covers : {35,8}*1680a
Permutation Representation (GAP) :
```s0 := (3,7)(4,8)(5,6);;
s1 := (2,3)(4,6)(5,7);;
s2 := (1,2)(3,4)(5,6)(7,8);;
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, s2*s0*s1*s2*s0*s1*s2*s0*s1*s2*s0*s1,
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1,
s0*s1*s0*s1*s2*s0*s1*s0*s1*s2*s0*s1*s0*s1*s2 ];;
poly := F / rels;;

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

```
References : None.
to this polytope