Geometric Crystallography: Modelling and Representation of Polyhedra

This paper explores the geometric matrices of crystals and their modeling from theoretical abstraction to the tangible concreteness of wooden and glass collections, dating from the Eighteenth and Twentieth centuries. The morphological characteristics of the crystals (regular or irregular polyhedra), the geometric ones (planes, axes, centers of symmetry) and the parametric ones (angular opening between the reference semi-axes, axial coordinates) are examined through the glass models, kept in the Michelangelo Educational Museum (Caserta, Italy), and through analog and digital different graphic representations used in the scientific field for speculative and educational purposes. The research has educational and design purposes: the study of crystals as polyhedra is useful to illustrate to students the abstractions of Geometry of solids and the graphic representations through Descriptive Geometry; the geometric matrices of crystals are the keys to scientifically control the cut of natural and artificial “new gems”, or of existing ones to increase their economic value; the geometry of polyhedra opens up to interesting design ideas in architecture, industrial design and fashion design. Finally, about to the rare glass models of the crystals preserved in the Michelangelo Museum, the problem arises of their conservation as well as of other similar specimens, ensuring their use in the educational field: the use through a digital archive that associates the 3D models of the crystals with the geometrical, physical and chemical data of the minerals would offer the starting point for the construction of a virtual educational museum.