DanA> If you imagine a 5x1 rectangular array of spheres centered above and lying upon a 4x2 rectangular array of spheres, likewise upon a 3x3, likewise upon a 2x4, likewise upon a 1x5 . . . then you see how a tetrahedral array of spheres can also be thought of as layers of square arrays of spheres each nestled in the hollows of the one below it. --Dan The second image, Manipulate[...], illustrates this with 7x1 etc instead of 5x1 etc. The slider controls the number of layers (four shown). You may find it amusing to analyze the actual mechanics of computing the Voronoi figure. %331 is the immediately preceding list of rules. (Why does Save as PNG discard the In and Out numbers?) --rwg On Fri, Jun 21, 2013 at 3:43 AM, Bill Gosper <billgosper@gmail.com> wrote:
I asked Neil if Kepler's sphere-stacking conjecture was about tetrahedral or square pyramids of cannonballs. He fooled with Mathematica briefly and said it doesn't matter <http://gosper.org/kepvor.png>. --rwg