#voderberg

Parkettierung nach Heinz Voderberg.

Heinz Voderberg found an interesting polygon with nine sides, having the interesting property that you can puzzle two of them together so that a third copy fits precisely between them. You can even fit a second copy of the same tile in between.

Using only this puzzle piece, there is an obvious (boring) way to tile the plane, simply by repeating the following pattern in both directions and placing the strips side by side.

The special property of the Voderberg tile, however, also allows it to tile the plane in the beautiful spiral-like pattern above, or in the circular pattern below. In both tilings, all tiles are congruent.

Heinz Voderberg discovered the first spiral monohedral tiling in 1936. His special tile is a non-convex enneagon and covers the plane exactly as shown above, in two spiral arms. Notice how the spirals need more and more switching in orientation of the tiles after each half turn.