Isometric Embedding of Mosaics Into Cubic Lattices

We review mosaics T (tilings of Euclidean plane by regular polygons) with respect to possible embedding, isometric up to a scale, of their skeletons or the skeletons of their duals T , into some cubic lattice Z n . The main result of this paper is the classication, given in Table 1, of all 58 such mosaics among all 165 mosaics of the catalog, given in [Cha89] and including all main classications of mosaics