# Chiral Polytope of Type {12,4}

Regular Cover :{12,4}*1200 with group SmallGroup(1200,961) = C52 ⋊ D4 x S3of order 1200
Rank : 3
Schlafli Type : {12,4}
Rotation Group : SmallGroup(120,36) = (C5 ⋊ C4) x S3 of order 120
Number of vertices, edges, etc : 30, 60, 10
If Aut({12,4}*1200)=<s0, s1, s2>, then this chiral polytope is ({12,4}*1200)/N, where
N=<s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2> of order 5
Facet : (Regular) 12-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^-1*sig2^-1*sig1^-1*sig2^-1, sig2*sig2*sig2*sig2, sig1*sig1*sig2^-1*sig1*sig1*sig1*sig2^-1*sig1,
sig1^-1*sig2^-1*sig2^-1*sig1^-1*sig2*sig1*sig1*sig2^-1*sig1^-1*sig1^-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, sig2*sig2*sig2*sig2,
sig1*sig1*sig2^-1*sig1*sig1*sig1*sig2^-1*sig1, sig1^-1*sig2^-1*sig2^-1*sig1^-1*sig2*sig1*sig1*sig2^-1*sig1^-1*sig1^-1 >;

```