The Genus-C⁴ Regular Map {6,4}

This regular map has four hexagonal faces, six 4-valent vertices, and 12 edges.

Its rotational symmetry group has order 48.

Its Petrie polygons are triangles and its holes are squares.

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

Another portrayal of it is below.