A packing of polyhedron in three-dimensional space. A polyhedron which can pack with no holes or gaps is said to be a space-filling polyhedron. Betke and Henk present an efficient algorithm for computing the density of a densest lattice packing of an arbitrary polyhedron, and explicitly calculate the densities for the Platonic and Archimedean solids.

Kelvin's conjecture | packing | space-filling polyhedron