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# Polytope of Type {8,28}

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {8,28}*1344d
if this polytope has a name.
Group : SmallGroup(1344,11289)
Rank : 3
Schlafli Type : {8,28}
Number of vertices, edges, etc : 24, 336, 84
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
Compact Hyperbolic Quotient
Locally Spherical
Non-Orientable
Related Polytopes :
Facet
Vertex Figure
Dual
Facet Of :
None in this Atlas
Vertex Figure Of :
None in this Atlas
Quotients (Maximal Quotients in Boldface) :
2-fold quotients : {8,14}*672a
4-fold quotients : {8,7}*336a
Covers (Minimal Covers in Boldface) :
None in this atlas.
Permutation Representation (GAP) :
```s0 := ( 1, 2)( 3, 5)( 4, 8)( 6, 7)( 9,11)(10,12);;
s1 := ( 2, 6)( 3, 8)( 4, 7)(10,12);;
s2 := ( 3, 4)( 5, 8)( 6, 7)( 9,10)(11,12);;
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*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,
s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0 ];;
poly := F / rels;;

```
Permutation Representation (Magma) :
```s0 := Sym(12)!( 1, 2)( 3, 5)( 4, 8)( 6, 7)( 9,11)(10,12);
s1 := Sym(12)!( 2, 6)( 3, 8)( 4, 7)(10,12);
s2 := Sym(12)!( 3, 4)( 5, 8)( 6, 7)( 9,10)(11,12);
poly := sub<Sym(12)|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*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,
s1*s2*s0*s1*s0*s1*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s1*s0*s2*s1*s0*s1*s0 >;

```
References : None.
to this polytope