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I Rn SCYE MATHEMAT I CAL RECREAT ! OIIS, 2 NABLA

He takes*,hich forms a bridge between two and three dimensions.

Fig.46.

the 12 pentominoes, but made from clbes 'Ln place of squares (Fig.a6).These can be assembled to form a block of size 3x4x5, though I haven'tconfirmed this. This puzzle has more aesthetic appeal to me than manyof the pentomino puzzles, on account of the synmetry. As mentioned inPart I of this article, six of the 12 pentominoes are unsyr.netrical,and have a different appearance when turneci over, so that it is possibleto considera larger set of 18 (or even a set of 36, if each is chequeredin its two possible ways), which are not allowed to be turned over.

Of cor:rse, there are many more than the 12r,solid pentominoes,'ofLehmer's puzzle. rf we include the essentially three-dimensional com-binations of five cubes, there are altogether )1, or ?{if we countreflexions as distinct. Here there is rnore ground for doing this, aswe cannot!rturn a piece over" without nraking a temporary trip into fourcl irnensions. From this last set

"t *t, we rnay reject @n the 4 whichhave a dimension of four or more units. and--t.}re-2-rrh,Lshi-oc+ud,6-e..$bck+f-Focr=tlbe peai-s-Sh113-26:u+ils_-asopgssed-La .+ha rr.r^L-2-1, The remaining 25 pieces may perhaps fit to-gether to form a cube of edge five units, though the model to demon-strate this has not yet been conrpleted.

Piet Hein, in inventing his 'rSoma', puzzle took 6 of the g ,solidtetrominoes" (r.jecting the row of four cubes and the ,,square,rof four

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