Voderberg Tile

thingiverse

This is an example of a Voderberg tile created by Heinz Voderberg. It has several interesting properties. It solves a problem posed by Karl Reinhardt: two of these tiles can completely enclose a tile of the same shape—and in fact, two of these tiles can include TWO tiles of the same shape. Interestingly, they can be assembled to make an infinite spiral tiling. (They can also be assembled to tile the plane periodically.)