Derivative structures based on the sphere packing

A significant number of non-molecular crystal structures can be described as derivative structures of sphere packings, with variable degrees of distortion. The undistorted sphere packing model with all the cavities completely occupied is the aristotype, from which an idealized model of the real structure can be obtained as a substitution, undistorted hettotype. The real structure can then be seen as a distorted derivative of the substitution hettotype. In this article we revive the symbolism introduced by Zoltai and Stout to describe the substitution hettotypes and compare these with the corresponding real structures. In most cases, the distortions are small or even negligible. For some structures, a significant departure from the substitution hettotype is observed, which however does not prevent to adopt the same description as a unifying scheme.