Abstract
Polytopes may be defined as the convex hull of finitely many points in n-dimensional space ℝn. They are fundamental objects in computational geometry. When studying polytopes, it soon becomes apparent that the proof of seemingly obvious properties often requires further clarification of the basic underlying geometric structures. An example of this is the major result that polytopes can also be represented as the intersection of finitely many affine half-spaces.
In this chapter the geometric foundations of polytopes and unbounded polyhedra will be presented from a computational viewpoint.
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Joswig, M., Theobald, T. (2013). Polytopes and Polyhedra. In: Polyhedral and Algebraic Methods in Computational Geometry. Universitext. Springer, London. https://doi.org/10.1007/978-1-4471-4817-3_3
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DOI: https://doi.org/10.1007/978-1-4471-4817-3_3
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