The Genus-3 Map {3,8}

The regular map S³{3,8} shown to the right has 32 triangular faces, 12 8-valent vertices, and 32 edges.

Its Petrie polygons have six edges, its holes have six edges, its 2nd-order Petrie polygons have eight edges, its 3rd-order holes have three edges, its 4th-order Petrie polygons have six edges, and its 4th-order holes have four edges.

It is the dual of S³{8,3}.