Abstract
Arrangements of lines in the plane and their higher-dimensional generalization, arrangements of hyperplanes in R d, are a basic geometric structure whose significance is comparable to that of convex polytopes. In fact, arrangements and convex polytopes are quite closely related: A cell in a hyper-plane arrangement is a convex polyhedron, and conversely, each hyperplane arrangement in R d corresponds canonically to a convex polytope in R d +1 of a special type, the so-called zonotope. But as is often the case with different representations of the same mathematical structure, convex polytopes and arrangements of hyperplanes emphasize different aspects of the structure and lead to different questions.
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© 2002 Springer-Verlag New York, Inc.
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Matoušek, J. (2002). Number of Faces in Arrangements. In: Matoušek, J. (eds) Lectures on Discrete Geometry. Graduate Texts in Mathematics, vol 212. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0039-7_6
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DOI: https://doi.org/10.1007/978-1-4613-0039-7_6
Publisher Name: Springer, New York, NY
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