Cogs can be arranged to correspond with the faces or edges of a
polyhedron and meshed to turn simultaneously.
The following arrangements are based on polyhedra with every vertex
having an even vertex order. This means that every vertex is met by an
even number of faces and edges. These polyhedra can be coloured using
just two colours with no neighbouring faces having the same colour.
This property also applies to the cogs, so neighbouring cogs can
always turn in opposite directions.