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 but two examples. The history of diamond cuts can be traced to the late Middle Ages, before which time diamonds were employed in their natural octahedral state—anhedral (poorly formed) diamonds simply were not used in jewelry. The first "improvements" on nature's design involved a simple polishing of the octahedral crystal faces to create even and unblemished facets, or to fashion the desired octahedral shape out of an otherwise unappealing piece of rough. This was called the "point cut" and dates from the mid 14th century; by 1375 there was a guild of diamond polishers at Nürnberg. By the mid 15th