Number 67 (Story #2), February 12, 1992 by Phillip F. Schewe and Ben Stein COPERNICAN CRYSTALLOGRAPHY , a new classification scheme for crystallography formulated by N. David Mermin of Cornell (607-255-9689), puts quasi-periodic materials such as quasicrystals (which form dodecahedral grains) on an equal footing with periodic crystals. Mermin does this by emphasizing the concept of indistinguishable---rather than identical---densities to denote crystallographic taxonomy. The kind of translation that defines microscopic periodicity in perfect crystals would then be just one among several possible translations that map one subregion into a nearby identical subregion. In Mermin's generalized scheme there would be no need to describe quasiperiodic materials as being three-dimensional sections of materials periodic in some higher-dimensional space. Mermin believes that resorting to such a "superspace" is analogous to the use of epicycles in pre-Copernican times to help explain the apparently odd movements of planets in an earth-centered astronomy. He suggests that "Ptolemaic" crystallography (centered on periodic crystals) should be abandoned. (Physical Review Letters, 24 Feb. 1992.)