Prismatic boron nitride nanorods have been grown on single crystal silicon substrates by mechanical ball-milling followed by annealing at 1300 °C. Growth takes place by rapid surface diffusion of BN molecules, and follows heterogeneous nucleation at catalytic particles of an Fe/Si alloy. Lattice imaging transmission electron microscopy studies reveal a central axial row of rather small truncated pyramidal nanovoids on each nanorod, surrounded by three basal planar BN domains which, with successive deposition of epitaxial layers adapt to the void geometry by crystallographic faceting. The bulk strain in the nanorods is taken up by the presence of what appear to be simple nanostacking faults in the external, near-surface domains which, like the nanovoids are regularly repetitive along the nanorod length. Growth terminates with a clear cuneiform tip for each nanorod. Lateral nanorod dimensions are essentially determined by the size of the catalytic particle, which remains as a foundation essentially responsible for base growth. Growth, structure, and dominating facets are shown to be consistent with a system which seeks lowest bulk and surface energies according to the well-known thermodynamics of the capillarity of solids.