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
Mineral is in six-fold coordination; its chemical formula can be expressed as AlAlSiO, to reflect its crystal structure. Andalusite has the second aluminium in five-fold coordination (AlAlSiO) and sillimanite has it in four-fold coordination (AlAlSiO). Differences in crystal structure and chemistry greatly influence other physical properties of the mineral. The carbon allotropes diamond and graphite have vastly different properties; diamond is the hardest natural substance, has an adamantine lustre, and belongs to the isometric crystal family, whereas graphite is very soft, has a greasy lustre, and crystallises in the hexagonal family. This difference is accounted for by differences in bonding. In