Subdivisions from primal and dual cones and polytopes (Q760015)

Giving a convex polytope P which contains the origin of \({\mathbb{R}}^ n\) in its interior and its polar polytope \(P^*\) \((=\{y\in {\mathbb{R}}^ n:\quad xy\leq 1\quad for\quad allx\in P\}),\) there is a 1-1 correspondence between the faces of P and \(P^*\) \((F\leftrightarrow F^*=\{y\in P^*:\quad xy=1\quad for\quad all\quad x\in F\}).\) Using this correspondence a tiling of \({\mathbb{R}}^ n\times [0,+\infty]\) with finitely many convex polyhedral cones with apexes at the origin is constructed (depending on a parameter).