Alejandro Zarzuelo Urdiales

Certified finite packings of Platonic solids: a generalized soft-to-rigid search and its computational development

We describe an open computational framework for placing congruent regular polyhedra in the smallest homothetic regular-polyhedral container found by numerical search. A cube-packing procedure introduced by Yohei Nakajima is generalized by replacing a convex piece P, with a center...

Finite polyhedral fits: discrete scale jumps, orientational domains, and contact structure in 351 certified constructions

Packing a finite number of congruent polyhedra inside a polyhedral container produces pronounced changes in required container size as the number of pieces increases. Some adjacent counts share a construction scale, while other additions require a substantial expansion. We study...