The Genus-C⁵ Regular Map {5,5}

This regular map has five hexagonal faces, five 6-valent vertices, and 15 edges. Each face borders each other face once, and each vertex is connected by one edge to each of the other vertices. (i.e. its vertex-multiplicity is 3).

Its is self-dual. It can be cantellated to give {5,4}. It the Petrie dual of the hemi-icosahedron.

Its rotational symmetry group is A5.

Its Petrie polygons are triangles, its holes are triangles, and its order-2 Petrie polygons are pentagons.

Each vertex is antipodal to a face and to an order-2 Petrie polygon. The edges form antipodal threesomess. The holes form antipodal pairs. The Petrie polygons form antipodal pairs.