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Polyhedral geometry as a basis for building structures and other materials systems. (English) Zbl 0883.51006

Polyhedra are usually described as a set of polygons enclosing together a portion of space. This definition is well in accordance with what architecture aims at. As a matter of fact most building structures are in their general shape (macroform) or in their structural configuration (microform) based on polyhedral geometry. It seems that at this moment a revival of the apprehension is noticeable by architects and artists of the polyhedron as an important medium for the expression of their ideas. Most of our buildings are momentarily based on the shape of the cube or of the prism, notwithstanding the fact that many other forms exist, which have more potentials and are much more interesting. The cube and the prism are members of a large family of regular and semi-regular solids: the so-called uniform polyhedra, of which representatives are found in nature itself in the form of crystals, viruses and radiolaria. Bees adopted the hexagonal cell apparently as an economic solution for their housing problem.

MSC:

51M20 Polyhedra and polytopes; regular figures, division of spaces
52B10 Three-dimensional polytopes
00A69 General applied mathematics
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