All Questions

Let us say I have the vertices of a polytope $V = \{v_1,\dots,v_k\} \subset \mathbb R^n$. Is it possible to write $V$ as intersection of half-spaces using the information from the vertices, i.e., can ...

What are efficient methods (polytime) to compute an approximation of the convex hull in high dimension (say, $30000$) for a given set of points? Edit: I am looking for an algorithm for getting the ...

I'm going by the Wikipedia definition for a 4-polytope. Do by definition, cells of 4-polytopes have to be a convex polyhedra? If not, then are there polyhedra with non-convex faces? If yes, is it the ...

Take a standard simplex or cube in $\mathbb R^n$. Is there a way to cover it with $O(poly(\log n))$ convex polytopes each describable by only $O(poly(\log n))$ half-plane inequalities? If not what ...