A Genus-C⁴ Regular Map {6,4}

This regular map has four hexagonal faces, six 4-valent vertices, and 12 edges. Each face borders each other face twice (i.e. its face-multiplicity is 2), and each vertex is connected by edges to four distinct other edges (i.e. its vertex-multiplicity is 1).

Its rotational symmetry group has order 48.

Its Petrie polygons are triangles, and its holes are squares.

Its dual is C⁴:{4,6}₃. Its Petrie dual is the octahedron.

Three more portrayals of it are below.