Maybe Asimov's concept better described as "Voronoi face count" or "Delaunay triangulation graph adjacencies". BCC has 8 nearest and 6 second-nearest neighbors [at sqrt(4/3) times the distance], all 14 Voronoi [truncated octahedron]. FCC has 12 nearest and 6 second-nearest [at sqrt(2) times the distance], but voronoi has only 12 faces [rhombic dodecahedron]. NewLatt has 10 nearest and 4 second-nearest neighbors [at sqrt(3/2) times the distance; sorry, this square is not an integer, but if multiply square by 2, then integer; I should have said, when defining "integral" lattice, that all squared distances are integer multiples of SOMETHING, but not nec. of the shortest squared distance]. I think NewLatt's Voronoi has 14 faces, kind of a distorted version of the BCC Voronoi region. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)