Diamond cubic strong isotropic property. Namely, for any two vertices "x" and "y" of the crystal net, and for any ordering of the edges adjacent to "x" and any ordering of the edges adjacent to "y", there is a net-preserving congruence taking "x" to "y" and each "x"-edge to the similarly ordered "y"-edge. Another (hypothetical) crystal with this property is the Laves graph (also called the K crystal, (10,3)-a, or the diamond twin). The compressive strength and hardness of diamond and various other materials, such as boron nitride, is attributed to the diamond cubic structure. Similarly truss systems that follow the diamond
Diamond cut the original shape of the rough stone, location of internal flaws or "inclusions", the preservation of carat weight, and popularity of certain shapes among consumers. The cutter must consider each of these variables before proceeding. Most gem-quality diamond crystals are octahedra in their rough state (see material properties of diamond). These crystals are usually cut into "round brilliants" because it is possible to cut two such stones out of one octahedron with minimal loss of weight. If the crystal is malformed or twinned, or if inclusions are present at inopportune locations, the diamond is more likely to receive a "fancy