Tiling the Space by Polycube Analogues of Fedorov’s Polyhedra

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.