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A branch of geometry dealing with convex sets and functions. Polytopes, convex bodies, discrete geometry, linear programming, antimatroids, ...
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Volume of caps of a polytope
Let $K$ be a polytope in $\mathbb R^d$, blow it up by a factor $\lambda>0$. For a unit vector $u \in \mathbb S^{d-1}$, $\lambda K$ has 2 support hyperplanes $H_1$ and $H_2$ with corresponding outward …