Figure 1. Strongly isotropic networks and their amorphous derivatives in three dimensions.

The WS cell of a diamond PhC (a) contains a 1-tree of dielectric material (green); the edges of the tree define a tetrahedral unit. Stacking of the WS cells generates the champion diamond PhC (b). Amorphous diamond (c) consists of deformed tetrahedral units connected in a CRN. Similarly, the WS cell of a single-network gyroid PhC contains a 2-tree (d), comprising dielectric material (blue), in which each vertex is a trihedron. When stacked, the WS cells generate a single-network gyroid PhC with a near-champion PBG (e). Amorphous gyroid (f) comprises deformed trihedral units connected in a CRN.