The Genus-C⁷ Regular Map {4,6}

This regular map has 15 square faces, 10 6-valent vertices, and 30 edges.

Its dual is C⁷{6,4}. Its Petrie dual is S⁵{5,6}.

Its rotational symmetry group is S5.

Its Petrie polygons are pentagons, its holes are triangles, its second-order Petrie polygons are triangles, and its 3rd-order holes as hexagons which traverse the same sets of three edhges twice.

Each vertex is antipodal to a 3rd-order hole. Each face is antipodal to a Petrie polygon. The faces form antipodal threesomes ‒ eacg threesome is shown in a single colour in the diagram to the right.