An octet truss is a three-dimensional framework formed by a finite slab of the 
-skeleton of the tetrahedral-octahedral
honeycomb. Its members bound interlocking regular
tetrahedra and regular octahedra.
Alexander Graham Bell used recursively assembled tetrahedral frameworks in kite structures (Bell 1903). R. Buckminster Fuller later developed and named the octet truss and patented a system of interlocking octahedra and tetrahedra for roofs, walls, and floors. His 1955 airplane-hangar project used the system as a lightweight framework for a long span (Fuller 1961, Museum of Modern Art 2007).
In an octet-truss subdivision, bisecting the polyhedron edges of a regular tetrahedron divides it into four smaller regular tetrahedra and one regular octahedron. The corresponding subdivision of a regular octahedron gives eight regular tetrahedra and six smaller regular octahedra. Alternatively, choosing one of the three polyhedron diagonals joining opposite polyhedron vertices divides the octahedron into four tetrahedra (Chang and Qin 2006).
Splitting each octahedron along one chosen polyhedron diagonal gives a recursive tetrahedral mesh with two tetrahedron shapes. A regular tetrahedron subdivides into four regular tetrahedra and four tetrahedra obtained by quartering its central octahedron. If the long edge of each latter tetrahedron is chosen first, it subdivides into two regular tetrahedra and six of the second type. Consequently, successive subdivisions produce only these two similarity classes (Zhang 1995).
