Interlocking Toroidal Tile for Tessellating R3

by Carlo H. Séquin

The two figures below show a simple toroidal tile with a small number of polyhedral faces that acts as a single tiling element to tile 3-space in a regular manner without voids. The first figure shows the single element and the second Figure shows a complete tile with two interlocked half-tiles to show the basic arrangement. Two more toroidal tiles will fit through the shown open holes. In general every toroidal tile embraces four other toroids that stand at right angles to each other.