Polyhedra and Honeycombs in a Coffered Ceiling in the Picasso Museum in Malaga.

This paper reflects upon the remarkable ceiling of the Picasso Museum in Malaga, an example of the wooden coffered ceilings built during the early Renaissance in Spain. The unusual design of the ceiling is based on octagons surrounded by four-pointed stars. This is used as the point of departure for a mathematical investigation of polyhedral forms. Two different polyhedra are constructed, conceived in such a way that the honeycombs generated by them, can be considered a polyhedral generalization of the planar pattern of regular octagons and four-pointed stars. Both are constructed by means of special truncations of a cube. The truncation procedure is extended to construct a polyhedral generalization of the planar pattern of four-pointed stars and 45° rhombuses; in this case, the polyhedron obtained is a variation of one of the star polyhedra drawn by Jamnitzer. The geometric honeycombs thus defined could be used as models for new designs.