Packing Polyhedra within Convex Sets

Abstract

This work addresses two problems related to packing identical regular polyhedra, focusing on triangles and squares. The first problem seeks to maximize the number of identical regular polyhedra that can be packed within a convex set or container.The second problem focuses on achieving the densest possible packing of a fixed number of identical regular polyhedra within a container of a given type. Both problems are modeled as nonlinear differentiable programming problems.