Questions tagged [convex-polytopes]

I am studying a large collection of lattice polytopes, all of them being simple and empty. The dimension can be any integer. The dilatation by $2$ gives non-empty polytopes. For many of these ...

Let $P\subset\Bbb R^d$ be a convex polytope. Its reduced realization space is the space of all combinatorially equivalent polytopes modulo projective transformations. I am interested in polytopes for ...

Consider Associahedron, consider graph build from its vertices and edges. Choose some vertex. Let us count the number of vertices on distances $k$ from the selected vertex. Write a generating ...

Encouraged by the positive solutions to my question, Tiling with one of each shape, I'd like to pose the $\mathbb{R}^3$ equivalent: Q. Is there a tiling of $\mathbb{R}^3$ by (bounded) polyhedra, one ...

Let $Q \subseteq R^n$ be a rational polyhedron and let $Q_I=Convexhull(Q \cap Z^n)$. By finite basis theorem, we have $Q=P+C$ for some rational polytope $P$ and finitely generated cone $C$ where $C=R_+...

I am currently reading Christer Ericson's Real-Time Collision Detection Book. The topic I'm particularly interested in, is the chapter about Discrete-orientation Polytopes (k-DOPs). In his words "...