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# Chiral Polytope of Type {7,14}

Regular Cover :{7,14}*1792d with group SmallGroup(1792,1083553) = (C26 ⋊ D7) x C2of order 1792
Rank : 3
Schlafli Type : {7,14}
Rotation Group : SmallGroup(112,41) = (C23 ⋊ C7) x C2 of order 112
Number of vertices, edges, etc : 8, 56, 16
If Aut({7,14}*1792d)=<s0, s1, s2>, then this chiral polytope is ({7,14}*1792d)/N, where
N=<s1*s2*s1*s0*s1*s2*s1*s0*s1*s0*s1*s2*s1*s2, s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s0*s1*s2*s1, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1> of order 8
Facet : (Regular) 7-gon
Vertex Figure : (Regular) 14-gon
Finitely Presented Group Representation of the Rotation Group(GAP) :
```F := FreeGroup("sig1","sig2");;
sig1 := F.1;;  sig2 := F.2;;
rels := [ sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig1*sig1*sig1*sig1*sig1,
sig1*sig1*sig2^-1*sig1*sig2^-1*sig2^-1*sig2^-1 ];;
rotpoly := F / rels;;

```
Finitely Presented Group Representation of the Rotation Group (Magma) :

```rotpoly<sig1,sig2> := Group< sig1,sig2 | sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig1*sig1*sig1*sig1*sig1*sig1*sig1,
sig1*sig1*sig2^-1*sig1*sig2^-1*sig2^-1*sig2^-1 >;

```