The figure shown and described below is **not** a regular map.
Each face borders the other five twice each; but for each face, there is
only one of the five others such that its two borders with it are a pair
of opposite sides. So these two borders are distinguishable from its
others, and the polyhedron is not edge-transitive.

This irregular map has six decagonal faces, of which three meet at each of its 20 vertices. It has 30 edges, and a Euler characteristic of -4. It is shown to the right.

Its dual is {10,3}.

Other regular maps on the genus-3 oriented surface.

Index to other pages on regular maps.

Some pages on groups

Copyright N.S.Wedd 2009