The figures shown and described here are **not** regular maps.
For the one on the left, three Petrie polygons have five edges
and one has 20, so it cannot be edge-transitive. For the one on
the right, each vertex is connected to all four other vertices,
two of them twice, so it is not edge-transitive.

These maps are in genus-6c (a sphere plus six crosscaps). They have six pentagonal faces, all meeting at each of five six-valent vertices. It has 15 edges, giving a Euler characteristic of -4.

If the central face in the diagram on the left, and its five
edges, are removed, we get the regular map
C^{6}:{20,4}.
If we do the same to the one on the right, we get an irregular
C^{6}:{20,4}

Other regular maps on the genus-C^{6} surface.

Index to other pages on regular maps.

Copyright N.S.Wedd 2009