Voderberg Mann Tiles

This tile was found by Casey Mann in 2002.
(The png drawing was made by the author.)

Two copies of the tile can surround a third copy completly.
The tile does not admit a tiling of the plane.

Reference: Casey Mann, (2002). A tile with surround number 2. The American Mathematical Monthly, Vol. 109, No. 4, pp. 383-388.

With a modified Voderberg tile it is possible to enlarge the small hooks and catches.