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Zbl 0946.05023
Hochberg, Robert; Reid, Michael
Tiling with notched cubes. (English)
[J] Discrete Math. 214, No.1-3, 255-261 (2000). ISSN 0012-365X

It was known [see {\it 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.
[Nikolai L.Manev (Sofia)]

MSC 2000:: *05B45 Tessellation and tiling problems
52C22 Tilings in n dimensions (discrete geometry)

Keywords: polyomino; tiling

Citations: Zbl 0143.44202

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