The Genus-2 Regular Map {10,5}

This genus-2 regular map, shown to the right, has one decagonal face, meeting five times at each of its two vertices. It has five edges, and a Euler characteristic of -2.

Its dual is {5,10}.

Its Petrie dual is the 5-hosohedron.

Its rotational symmetry group is D10.

Faces share vertices with themselvesFaces share edges with themselves The face shares all its vertices and all its edges with itself. Some readers may consider that this invalidates it as a regular map.

Its holes have ten edges. Its Petrie polygons have two edges.

Antipodal Faces and Vertices

Each vertex is antipodal to the other.


Other regular maps on the genus-2 oriented surface.
Index to other pages on regular maps.
Some pages on groups

Copyright N.S.Wedd 2009