Thanks for setting me straight on this, Adam. Sheesh, the HCP looks so much like a lattice packing that I was fooled. --Dan P.S. This reminds me of another configuration of points in 3-space that isn't a lattice, though it's often called one informally by chemists and crystallographers: the arrangement of atoms in a diamond. This is kind of tricky to visualize fully. On 2013-06-23, at 3:11 AM, Adam P. Goucher wrote:
From: Dan Asimov
Just to add to this, Wikipedia reminds me that there are two distinct lattice packings
Only the face-centred cubic (a b c a b c ...) is a lattice packing; the hexagonal close packing (a b a b a b ...) is not a lattice. (A lattice in R^n requires that the group of translational symmetries act transitively on the points, whereas HCP has two orbits.)