Tiling with notched cubes
It was known [see \textit{S. W. Golomb}, J. Comb. Theory 1, 280-296 (1966; Zbl 0143.44202)] that any polyomino which tiles a rectangle also tiles a larger copy of itself. It is not natural to expect the converse to be true but there has been no counterexample. In the paper such counterexamples are found for dimensions \(d>2.\) The author exhibits a polycube (a ``notched cube'') that tiles a large copy of itself, but does not tile any box. He obtains related results about tiling with this figure as well.
scientific article; zbMATH DE number 1423748