The Genus-3 non-Regular Map {3,14}

This genus-3 map is not regular. Its faces fall into two sets, which are not interchanged by rotations. It is therefore not dart-transitive. This genus-3 regular map has 14 triangular faces, all 14 meeting at each of its three vertices. It has 21 edges, and a Euler characteristic of -4. It is shown to the right.

Its Petrie polygons have six edges.

Each pair of vertices is connected by seven edges.

Its dual is S³{14,3}.

The edges of this regular map can be 3-coloured, and the faces 2-coloured, as shown in the diagram.