Hochberg, Robert; Reid, Michael Tiling with notched cubes. (English) Zbl 0946.05023 Discrete Math. 214, No. 1-3, 255-261 (2000). It was known [see 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. Reviewer: Nikolai L.Manev (Sofia) Cited in 2 Documents MSC: 05B45 Combinatorial aspects of tessellation and tiling problems 52C22 Tilings in \(n\) dimensions (aspects of discrete geometry) Keywords:polyomino; tiling Citations:Zbl 0143.44202 PDFBibTeX XMLCite \textit{R. Hochberg} and \textit{M. Reid}, Discrete Math. 214, No. 1--3, 255--261 (2000; Zbl 0946.05023) Full Text: DOI