**This is not a regular map.** It is in genus-C^{6}
(a sphere plus six crosscaps). It has five square faces, each
meeting two of the others twice each. It has one vertex and 10
edges, giving a Euler characteristic of -4.

Its dual is C^{6}:{20,4}.

It has one Petrie polygon with 10 edges and two each with five edges. Each edge participates in the 10-sided Petrie polygon and in one five-sided one. Its holes have two edges.

Each face shares all its vertices with itself. The edges join a vertex to itself. Some readers may consider that this invalidates it as a regular map.
If we choose any one face in the diagram, and remove it and its four edges,
we get the regular map S^{3}:{12,12}.

This map is similar in some respects to the above. Its Petrie polygons all have five edges, and its holes both have ten.

Its dual is 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