Interesting problem! I think I have a deterministic construction, although the proof that it satisfies (c) involves a huge amount of hand-waving. It satisfies (a), (b), (c), and (d), though not (e) or the "grog condition". I agree that it should be possible to satisfy the grog condition as well, though I'm less sure about (e); the sort of construction I use would result in "crystal defects" in what is mostly a square lattice. Want to get together for lunch sometime? If you're willing to travel up here (near the Burlington Mall), there's a nice Thai place. Andy