The Genus-3 Map {6,4}

This regular map has 12 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 Petrie dual is S³:{12,4}.

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. However, it is not a regular map. Some of its holes have two edges, some have three.