The Genus-3 Map {9,3}

The figure shown and described below is not a regular map. Each face borders seven other faces, one of them three times, so it is not edge-transitive.

This genus-3 regular map has eight nonagonal faces, of which three meet at each of its 24 vertices. It has 36 edges, and a Euler characteristic of -4. It is shown to the right.

The diagram was constructed from that for S³:{7,3}₈ by merging sets of three faces that shared a vertex, and erasing their common edges. This has left sharp angles within edges, as seen below. These sharp angles were then removed.

Its dual is S³:{3,9}.