# Chiral Polytope of Type {4,4}

Regular Cover :{4,4}*800 with group SmallGroup(800,1058) = C52 ⋊ ((C24) ⋊ C2)of order 800
Rank : 3
Schlafli Type : {4,4}
Rotation Group : SmallGroup(80,34) = D10 ⋊ C4 of order 80
Number of vertices, edges, etc : 20, 40, 20
If Aut({4,4}*800)=<s0, s1, s2>, then this chiral polytope is ({4,4}*800)/N, where
N=<s1*s0*s1*s2*s1*s0*s1*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s2> of order 5
Facet : (Regular) 4-gon
Vertex Figure : (Regular) 4-gon
Finitely Presented Group Representation of the Rotation Group(GAP) :
```F := FreeGroup("sig1","sig2");;
sig1 := F.1;;  sig2 := F.2;;
rels := [ sig1*sig1*sig1*sig1, sig1^-1*sig2^-1*sig1^-1*sig2^-1, sig2*sig2*sig2*sig2,
sig1^-1*sig1^-1*sig2*sig1^-1*sig2^-1*sig1*sig2^-1*sig2^-1*sig1*sig2^-1*sig1*sig2^-1 ];;
rotpoly := F / rels;;

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

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

```