  A locally finite face-to-face tiling of euclidean d-space by convex polytopes
is called combinatorially multihedral if its combinatorial automorphism group
has only finitely many orbits on the tiles. The paper describes a local
characterization of combinatorially multihedral tilings in terms of centered
coronas. This generalizes the Local Theorem for Monotypic Tilings, established
in an earlier paper, which characterizes the case of combinatorial
tile-transitivity.
