Tetrahedron packing using optimization

Details

Supervisors

Glineur, François

Faculty

Ecole polytechnique de Louvain

Degree label

Master [120] : ingénieur civil en mathématiques appliquées, à finalité spécialisée

Abstract

During this master thesis, we studied the tetrahedron packing problem using a purely optimization based approach. This problem consists in filling the space as densely as possible using regular unit edge tetrahedra that has fascinated humans for centuries. We start by introducing packing problems and the specific one about tetrahedron as well as their relevance in other domains. We continue by presenting an overview on the literature on the subject from the prism of the evolution of the packing density. Then, we present our approach, how it came about and how we managed to build models to put it into reality. Then taking our best model, we solve it using the IPOPT solver and apply a set of procedures in order to reach the best packing possible. The best we managed to get is 0.818978 not beating the best result to date but not being too far off. The different results are compared and analyzed. To finish this thesis and as a little sidetrack, we present how we performed a physical experiment using tetrahedral dices.