DENSELY PACKED RECTANGULATIONS

Rectangulations include packings of rectangles in two dimensions and p ackings of cuboids (3-rectangles) in three dimensions. Spatial layouts of this type are used in architectural and engineering design. In thi s paper we examine the spatial relations between the lines, planes, an d volume elements in these designs. It is shown how to describe rectan gulations as shapes in product algebras. Spatial relations, particular ly adjacencies between areas, volumes, maximal planes, or maximal line s are used to represent rectangulations. More general properties of th ese spatial relations are derived. Generative properties of rectangula tions are established which distinguish those 3-rectangulations which have an essentially two-dimensional character.