Rhombohedra

Rhombohedra are produced by varying one body diagonal of a cube while keeping the edge length constant. The result is an oblate rhombohedron if the diagonal is shortened, and a prolate rhombohedron if the diagonal is extended. The control actually varies the ratio of the face diagonals.

The rhombohedron is divided into an octahedron and two tetrahedra. The unit consisting of one octahedron and one tetrahedron, sometimes referred to as an octet truss, is widely used in architecture to produce lattice girders.

Each oblate rhombohedron has a prolate counterpart, which has the same rhombic faces. Pairs of such counterparts are often found in the geometry of quasicrystals.

The minimum diagonal ratio of the oblate rhombohedra is 1/when all the faces flatten into the same plane. The diagonal ratio of the prolate rhombohedra is not limited; their maximum body diagonal is 3.