The Genus-3 Map {4,6}

This regular map has 12 square faces, eight 6-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. Its holes have four edges. Its 2nd-order Petrie polygons have six edges. Its 3rd-order holes have two edges.

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

Its dual is S³:{6,4}.