  We give a complete classification of hexagonal tilings and locally C6 graphs,
by showing that each of them has a natural embedding in the torus or in the
Klein bottle. We also show that locally grid graphs are minors of hexagonal
tilings (and by duality of locally C6 graphs) by contraction of a perfect
matching and deletion of the resulting parallel edges, in a form suitable for
the study of their Tutte uniqueness.

Combinatorics