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# Tag Archives: polyhedra

## ‘Shear’ convex polyhedra: solution

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

## ‘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

## 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