A Genus-3 Map {10,3}

The figure shown and described below is not a regular map. Each face borders the other five twice each; but for each face, there is only one of the five others such that its two borders with it are a pair of opposite sides. So these two borders are distinguishable from its others, and the polyhedron is not edge-transitive.

This irregular map has six decagonal faces, of which three meet at each of its 20 vertices. It has 30 edges, and a Euler characteristic of -4. It is shown to the right.

Its dual is {10,3}.