A facet of a full-dimensional convex polytope in is a face of dimension . Each irredundant supporting closed half-space defines one facet.
If and a convex polytope satisfies , then it has at least facets. Its outward facet normals define spherical caps covering the unit sphere; the spherical cap area upper bound supplies the estimate.
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The term "facet" can have different meanings depending on the context in which it is used. Here are a few common interpretations: 1. **General Definition**: A facet refers to one side, aspect, or feature of something. It can describe any one of the many parts that make up a whole. 2. **Geology and Gemology**: In the context of gemstones, a facet is one of the flat polished surfaces on a cut gem.