Octet

Cubic cellular automaton under a binary XOR rule, mapped to an octahedron-tetrahedron honeycomb with every cell centered on an integer Cartesian coordinate. There's an intimate connection between this octet geometry — the dual of the face-centered cubic lattice found with e.g. close-packed spheres, what Bucky Fuller called the isotropic vector matrix — and orthogonal cubic tiling. These two seemingly disparate geometries are bound together by a shared set of symmetries in three-dimensional space — symmetries ultimately rooted in their common hexagonal heritage.