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# Chiral Polytope of Type {4,4}

Regular Cover :{4,4}*400 with group SmallGroup(400,211) = C52 ⋊ D4 x C2of order 400
Rank : 3
Schlafli Type : {4,4}
Rotation Group : SmallGroup(40,12) = (C5 ⋊ C4) x C2 of order 40
Number of vertices, edges, etc : 10, 20, 10
If Aut({4,4}*400)=<s0, s1, s2>, then this chiral polytope is ({4,4}*400)/N, where
N=<s0*s1*s0*s2*s1*s0*s1*s2*s1*s0*s1*s2*s1*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*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*sig2^-1*sig1*sig2^-1 >;

```