By a combinatorially regular polyhedron of index two the author understands a polyhedral realization (self-intersections allowed) in \(E^ 3\) of a regular map such that the (metrical) symmetry group is a subgroup of index 2 of the (combinatorial) automorphism group. In this paper, a new regular polyhedron of this kind is found; it has 20 vertices (those of a regular dodecahedron), 60 edges, 20 hexagonal faces (with self-intersections), and thus genus 11. The main result says that there are exactly 5 (orientable) regular maps which can be realized by a combinatorially regular polyhedron of index 2 (the other four of these were known before), and the realizations are metrically unique up to dilatations.