Polygons, polyhedra, polytopes

Marcel Berger ()
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Marcel Berger: IHÉS, Bures-sur-Yvette, Institut des Hautes Études Scientifiques

Chapter Chapter VIII in Geometry Revealed, 2010, pp 505-561 from Springer

Abstract: Abstract The polytopes subj Polytopes are, by definition, the convex envelopes of finite sets of points of an affine space. When this space is of dimension 2 (a plane), we speak of polygons; subj Polygon if the dimension is 3, we speak of polyhedra subj Polyhedron , and from then on – or from the very beginning – of polytopes. We are thus dealing with objects that are simplest after triangles. Now a detailed study of polyhedra is very recent. If we exclude the fundamental book of Steinitz name Steinitz , Ernst from 1934 and his papers from between 1906 and 1928, we find practically nothing on polyhedra before the 1960s.

Keywords: Regular Polygon; Hyperbolic Geometry; Combinatorial Type; Chapter VIII; Convex Envelope (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/978-3-540-70997-8_8

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