The description of octahedral crystals using five parameters

Acta Crystallogr A Found Adv. 2024 Jul 1. doi: 10.1107/S2053273324003097. Online ahead of print.

Abstract

The shape of a flat-faceted octahedral crystal can be uniquely defined by the measured distances between pairs of its parallel facets and the length of one of its false edges. In total, only five numerical values are involved in this approach. Some interdependencies of parameters that allow one to control the correctness of measurements were derived. The proposed method is suitable for describing the shape as full-faceted, or as incomplete octahedral crystals (e.g. diamond) with unequally developed facets. This so-called `real crystal form' can be considered as one of the typomorphic features of minerals, connecting the dissymmetry to the anisotropy of the host rock. The measurement results can be used in crystallo-morphological analysis, restoration of the lost crystal shape in the case of man-made damage and in the practice of diamond prospecting.

Keywords: diamond; geometry; morphology; octahedra; real form.