Nice article. It is worth pointing out that many of the maximally connected clusters are components of the hexagonal close-packed (HCP) lattice. This includes the symmetric version of the flexible n=9 cluster, as well as the n=10, 11, 12 rigid clusters that derive from it. HCP is the lower-symmetry twin of the face-centered cubic (FCC) lattice favored by fruit-sellers throughout history. I suspect that none of the maximal clusters are components of FCC beyond n=4.
posted by Aidan Thompson
November 9, 2012
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