Genus-C⁶ Maps {5,6}

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 C⁶:{20,4}. If we do the same to the one on the right, we get an irregular C⁶:{20,4}