A Genus-C6 non-Regular Map {4,20}

This is not a regular map. It is in genus-C6 (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 C6:{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.

Faces share vertices with themselvesVertices share edges with themselvesEach 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 S3:{12,12}.

A Related Irregular map {20,4}

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 C6:{20,4}.

Other regular maps on the genus-C6 surface.
Index to other pages on regular maps.

Copyright N.S.Wedd 2009