An Aperiodic Pair of Tiles inEnfor Alln ≥ 3

We give a set of only two tiles inEnfor eachn ≥ 3; these sets of tiles admit only non-periodic tilings inEn. The construction is based on similarities of the cubic lattice; a two-dimensional analogue of the construction can be found in Goodman-Strauss, Europ. J. Combinatorics (to appear).