Posted by hexnet -

In this image we see the symmetry group D6 of a regular hexagon. The hexagon can be rotated six ways, and reflected six ways. Note that any combination of two or more of these operations will still result in one of these twelve configurations. While rotations are commutative in two dimensions, reflections are not, so any composition of symmetries involving reflection is dependent on the order in which they are applied. In the table above, the row operation is applied before the column operation.