Q: What is the densest packing of spheres in a box? A: Depends on the box.
This Demonstration shows the number of unit diameter spheres that can fit in a given box, using one of the lattices SC, FCC, BCC, or HCP (simple cubic, face-centered cubic, body-centered cubic, or hexagonal close-packed). For a sufficiently large box, FCC gives the densest packing. For many small boxes, a denser non-lattice packing exists.