The figures shown and described here are **not** regular maps.
For the one on the left, one Petrie polygons has 15 edges, one has
ten, and one has five, so it cannot be edge-transitive. For the one
on the right, each vertex is connected to one other vertex once
and to two others twice each, so it cannot be edge-transitive.

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

Their duals are shown at C^{6}:{5,6}.

If the central vertex in the diagram, and its five edges, are removed
from the one on the left, 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