Fig. 3.

Contour maps of free energy for ${\mathrm{\Delta }}_{323}$ in (A) FCC, (B) SC, and (C) BCC. The perfect space-filling (Voronoi) shape, indicated by a filled circle in each panel, is different from any of the optimal shapes determined from simulation, even up to densities of $0.99$. (D–F) The densest packing surface reported in ref. 38 in the regions closest to the space-filling shapes for (D) FCC, (E) SC, and (F) BCC. The dashed lines in B, C, E, and F denote discontinuities in the derivative of the dense filling surface.