(color online) (a) The building blocks of a hyperhoneycomb with four atoms per unit cell. They are located at , , , and each atom has three neighbors connected by 120° bonds. Atoms 1 and 2 form the vertical building block, atoms 3 and 4 constitute the horizontal building block. The two blocks are connected by bonds along the z-direction. (b) The simplest 3D generalization of the hyperhoneycomb lattice. The four-site unit cell and primitive translation vectors are indicated, i.e., , , .