Tag Archives: polyhedra

‘Shear’ convex polyhedra: solution

Here I describe the solution to the problem from the last post. Spoilers! Advertisements

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‘Shear’ convex polyhedra

I came up with what seems quite a beautiful geometric construction solving the problem described below. On a compact convex set    consider the function where we denote  In other words, “hanging” in the point    we measure the “width” of the … Continue reading

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Cutting hypercube by an affine subspace

Fix an integer    Cut hypercube    with an arbitrary  -dimensional affine subspace    of general position.  How many vertices    has the obtained polyhedron? It occurs that    grows polynomially, and not exponentially, with    The goal of this … Continue reading

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