Tiling the Space by Polycube Analogues of Fedorov’s Polyhedra

Article type: Research Article

Authors: Gambini, Ian^a | Vuillon, Laurent^{b; *}

Affiliations: [a] Laboratoire d’Informatique Fondamentale (LIF), Aix-Marseille Université, 13288 Marseille Cedex 9, France. ian.gambini@univ-amu.fr | [b] Laboratoire de mathématiques, CNRS UMR 5127, Université de Savoie Mont Blanc, 73376 Le Bourget-du-lac Cedex, France. Laurent.Vuillon@univ-smb.fr

Correspondence: [*] Address for correspondence: Laboratoire de mathématiques, CNRS UMR 5127, Université de Savoie Mont Blanc, 73376 Le Bourget-du-lac Cedex, France

Abstract: We investigate minimal polycubes in terms of volume that tile the ℝ3 space like the Fedorov’s polyhedra. In fact the 5 Fedorov’s polyhedra are convex polyhedra that tile the space by translation and we construct geometrical discrete objects formed by union of cubes with the same number of faces than the Fedorov’s polyhedra.

Keywords: Tilings of ℝ³, polycubes, tilings by translation, Fedorov’s polyhedra, lattice periodic tilings

DOI: 10.3233/FI-2016-1381

Journal: Fundamenta Informaticae, vol. 146, no. 2, pp. 197-209, 2016