Polycubes are the three-dimensional analogues of the planar polyominoes: Every cube must be joined to at least one other cube by one full face. Piet Hein's 1936 Soma cube is an early example of an object composed entirely of polycube parts. In Martin Gardner's September 1958 Scientific American piece, the Soma cube was profiled — whereupon it enjoyed a flurry of interest leading up to a plastic Parker Brothers version in the summer of 1969. I own a beautiful skewed-Soma puzzle fashioned out of parallelepiped wooden stock: It's somewhat more difficult to solve than the right-angled polycube version!

In my picture, the cube on the left is composed of 25 identical Y-pentacube pieces and the one on the right is composed of 25 identical N-pentacube pieces. In each cube, one piece has been removed from the top layer (lower-left edge) and placed on the top-face. Neither cube is easy to solve and the finished product does not hold together particularly well. (A container would help.) The two cubes (and a slightly smaller, darker N-pentacube version, not shown) were gifts from Glenn Refling, circa 1980.