The Genus-3 Regular Map {7,14}

This genus-3 regular map, shown to the right, has two heptagonal faces, each meeting itself six times at each vertex. It has seven edges, and a Euler characteristic of -2.

Its dual is {14,7}. Its Petrie dual is the 7-hemihosohedron.

Its rotational symmetry group is D14.

The face shares all its vertices with itself. Some readers may consider that this invalidates it as a regular map.

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

Antipodal Faces and Vertices

The faces are antipodal to one another. The seven edges form a single antipodal set. Rotating any one edge about its centre causes every other edge to remain where it is and rotate about its own centre: this is the involution of its rotational symmetry group.