Approximating polyhedra in codimension one spheres embedded insnby tame polyhedra

Approximating Embeddings of Polyhedra in Codimension Three ( J )

Let F be a p-dimensional polyhedron and let Ç be a PL qmanifold without boundary. (Neither is necessarily compact.) The purpose of this paper is to prove that, if q — p > 3, then any topological embedding of P into Q can be pointwise approximated by PL embeddin-gs. The proof of this theorem uses the analogous result for embeddings of one PL manifold into another obtained by Cernavskii and Mille...

Approximating polyhedra with sparse inequalities

In this paper, we study how well one can approximate arbitrary polytopes using sparse inequalities. Our motivation comes from the use of sparse cutting-planes in mixed-integer programing (MIP) solvers, since they help in solving the linear programs encountered during branch&-bound more efficiently. However, how well can we approximate the integer hull by just using sparse cutting-planes? In ord...

Superspheres: Intermediate Shapes between Spheres and Polyhedra

Using an x-y-z coordinate system, the equations of the superspheres have been extended to describe intermediate shapes between a sphere and various convex polyhedra. Near-polyhedral shapes composed of {100}, {111} and {110} surfaces with round edges are treated in the present study, where {100}, {111} and {110} are the Miller indices of crystals with cubic structures. The three parameters p, a ...

Confined packings of frictionless spheres and polyhedra

By means of numerical simulations, we study the influence of confinement on three-dimensional random close packed (RCP) granular materials subject to gravity. The effects of grain shape (spherical or polyhedral) and polydispersity on this dependence are investigated. In agreement with a simple geometrical model, the solid fraction is found to decrease linearly for increasing confinement no matt...

polyhedra ∗