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