Questions?
See the FAQ
or other info.

# Chiral Polytope of Type {4,12}

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

```