A real rhombic dodecahedron: morphology and crystal shape variations.

Abstract

We propose a novel geometric characterization method for flat-faceted crystals bounded by a single simple crystallographic form - the rhombic dodecahedron. The approach utilizes distances between six pairs of parallel facets and the lengths of three false edges (out of six possible) resulting from anisotropic crystal growth. Our study has established the existence of exactly 34 combinatorially distinct, full-faceted real rhombic dodecahedra. For each type, we determined the range of crystal shape variations using the semi-axial lengths of the minimal-volume circumscribed ellipsoid. The results demonstrate that all real rhombic dodecahedra, except for eight special forms, can exhibit the complete spectrum of possible shape variations. These eight exceptional forms cannot develop tabular morphologies with bidirectional isometry. The obtained results provide valuable tools for precise analysis of rhombic dodecahedral crystal morphology and for establishing morphogenetic correlations between the degree of crystal distortions and the dissymmetry of the crystal-forming environment. This information is relevant for assessing the typomorphic features of natural diamonds, garnets, sodalites and magnetite crystals, as well as their synthetic analogs and other chemical compounds.