The Genus-3 Map {6,4}

This regular map has eight hexagonal faces, 12 4-valent vertices, and 24 edges. Its Euler characteristic is -4. It is shown to the right.

Its rotational symmetry group has order 48.

Its Petrie polygons have six edges, and its holes have four edges.

Its antipodal sets are (2V), (2F), (2E).

Its dual is S³:{4,6}.

An Irregular Genus-3 Map {6,4}

The figure shown here is not a regular map. Some of its holes have two edges, some have three.

The map shown to the right also has eight hexagonal faces, 12 4-valent vertices, and 24 edges.