Geodesic
On the Existence of Shapes of Roofs
Journal for geometry and graphics, Tome 8 (2004) no. 2, pp. 185-198.

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 51N05, 52B05, 05C90, 68U05
Mots-clés : Geometry of roofs, generalized polygon, k-connected generalized polygon, regular graphs, Euler formula for regular roofs, classification of shapes of roofs 
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     author = {E. Kozniewski },
     title = {On the {Existence} of {Shapes} of {Roofs}},
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     pages = {185--198},
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     number = {2},
     year = {2004},
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E. Kozniewski . On the Existence of Shapes of Roofs. Journal for geometry and graphics, Tome 8 (2004) no. 2, pp. 185-198. http://geodesic.mathdoc.fr/item/JGG_2004_8_2_JGG_2004_8_2_a5/