The diamond cubic is sometimes called the "diamond lattice" but it is not, mathematically, a lattice: there is no translational symmetry that takes the point (0,0,0) into the point (3,3,3), for instance. However, it is still a highly symmetric structure: any incident pair of a vertex and edge can be transformed into any other incident pair by a congruence of Euclidean space. Moreover, the diamond crystal as a network in space has a 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 K4 crystal, (10,3)-a, or the diamond twin).