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Convex polytopes are the convex hulls of a finite set of points in Euclidean spaces. They have rich combinatorial, arithmetic, and metrical theory, and are related to toric varieties and to linear programming
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Graduate level convexity - Intersection of an r-polytope with a hyperplane is an r-1 polytope
I am trying to follow Roger Webster's Convexity 's proof of Euler's celebrated result on the relationship between the number of faces of a polytope. An image of the proof is here.
In the course of the …