If you were to sit down with a pile of beads and try to build a big HCP stack and a big FCC stack layer by layer, you'd quickly understand why the densities are

If you were to sit down with a pile of beads and try to build a big HCP stack and a big FCC stack layer by layer, you'd quickly understand why the densities are the same. The bottom two layers (call them A and B) are identical between the two (without loss of generality), but you then have two distinct ways to proceed. For HCP, you shift back and add a layer identical to A (that is, the beads of the third layer are directly above the beads of the first) and then repeat, making an ABABAB... pattern. For FCC, you shift to the one allowed position that is not identical to A, making an ABCABC... pattern. (Fig. 1 of this Wikipedia article is at least a little useful for visualizing this: http://en.wikipedia.org/wiki/Close-packing_of_equal_spheres http://en.wikipedia.org/wiki/Close-packing_of_equal_spheres)