A Genus-3 Map {18,3}

The figure shown and described here is not a regular map. Each face borders itself along six edges and the other along 12. An edge which a face shares with itself is distinguishable from an edge which does not, so the polyhedron is not edge-transitive.

This irregular map has two 18-gonal faces, 12 vertices, and 18 edges.

Its dual is {18,3}.

Each face shares some vertices and some edges with itself. Some readers may consider that this invalidates it as a map.