3D Shape Grammar of Polyhedral Spires

Any random words can be put together - but in most cases they would not constitute a meaningful sentence. Similarly, any geometry can be used as the shape of a building or an architectural element, but in most cases tradition, aesthetics, and practice strongly restrict this theoretical freedom. The shapes of the spires of Western European medieval churches show a high variability - yet they use only a limited portion of the infinite set of potentially possible polyhedral or conical shapes. In this paper a generalized classification system of polyhedral spire shapes is presented as a kind of 3D shape grammar. This system can be used for describing the roof-shapes themselves - just like phonetic symbols can be used to represent the qualities of an oral language. At the same time the suggested notation system can hopefully provide unambiguous descriptions that can even be used in automated CAD modelling.