The Genus-2 Regular Map {4,6}

This regular map has four vertices, six hexagonal faces, and twelve edges.

Its rotational symmetry group is C3⋊ D8.

Its dual is {6,4}. Its double cover is S³:{4,6}. Its Petrie dual is S⁴:{12,6}.

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