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 Zn. The main result of this paper is the classi0cation, given in Table 1, of all 58 such mosaics among all 165 mosaics of the catalog, given in Chavey (Comput. Math. Appl. 17 (1989) 147) and including all main classi0cations of mosaics. c © 2002 Elsevier Science B.V. All rights reserved.