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In our third chapter, exercises treating various properties of n-dimensional convex polytopes (i.e., of n-dimensional convex hulls of finite point sets) are presented. Partial topics and basic notions referring to polytope theory and presented here are Minkowski sums of polytopes, polyhedral sets (polyhedra), diameters of polytopes, their face lattice, the role of partially ordered sets, (orthogonal) projections, lattice polytopes, Steiner symmetrals of polytopes, geometric properties of simplices, and decompositions of general polytopes into simplices.

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A First Look into Polytopes

  • 章节

  • 发表日期：

    2025年

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  • Vitor Balestro,
  • Horst Martini,
  • Ralph Teixeira

摘要

In our third chapter, exercises treating various properties of n-dimensional convex polytopes (i.e., of n-dimensional convex hulls of finite point sets) are presented. Partial topics and basic notions referring to polytope theory and presented here are Minkowski sums of polytopes, polyhedral sets (polyhedra), diameters of polytopes, their face lattice, the role of partially ordered sets, (orthogonal) projections, lattice polytopes, Steiner symmetrals of polytopes, geometric properties of simplices, and decompositions of general polytopes into simplices.