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Journal for Geometry and Graphics 08 (2004), No. 2, 185--198
Copyright Heldermann Verlag 2004

On the Existence of Shapes of Roofs

Edwin Kozniewski
Institute of Civil Engineering, Engineering Graphics and Computer Methods Division, Bialystok University of Technology, Bialystok, Poland

Roofs considered in this article are defined as special geometric polyhedral surfaces, on the basis of two assumption: (1) all eaves of a roof form a planar (simply connected or k-connected) polygon called the base of this roof, (2) every hipped roof end forms the same angle slope with the (horizontal) plane which contains the base of this roof. Basing on the Euler formula for regular roofs formulated and proved in a previous paper we formulate properties which enable a study of the shapes of roofs. We indicate how these properties may be used to analyse the shapes of roofs. We suggest a method of classification and a detailed classification of shapes of roofs for polygons with a small number of edges.

Keywords: Geometry of roofs, generalized polygon, k-connected generalized polygon, regular graphs, Euler formula for regular roofs, classification of shapes of roofs.

MSC: 51N05; 52B05, 05C90, 68U05

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