A Genus-C⁴ Regular Map {6,4}

This regular map has four hexagonal faces, six 4-valent vertices, and 12 edges. Each face borders two other faces twice each (i.e. its face-multiplicity is 2), and each vertex is connected by two edges to each of two other edges (i.e. its vertex-multiplicity is also 2).

Its dual is C⁴{6,4}₆. It is cantankerous, see W89. It is self-Petrie dual.

Its rotational symmetry group has order 48.

Its Petrie polygons are hexagons, its holes are squares, its order-2 Petrie polygons are triangles, and its order-3 holes are digons.

It is cantankerous^L02.

Another image of it is below.