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't confirmed this. This puzzle has more aesthetic appeal to me than many of the pentomino puzzles, on account of the synmetry. As mentioned in Part I of this article, six of the 12 pentominoes are unsyr.netrical, and have a different appearance when turneci over, so that it is possible to considera larger set of 18 (or even a set of 36, if each is chequered in its two possible ways), which are not allowed to be turned over. Of cor:rse, there are many more than the 12r,solid pentominoes,'of Lehmer's puzzle. rf we include the essentially three-dimensional com- binations of five cubes, there are altogether )1, or ?{if we count reflexions as distinct. Here there is rnore ground for doing this, as we cannot!rturn a piece over" without nraking a temporary trip into four cl irnensions. From this last set "t *t, we rnay reject @n the 4 which have 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_-as opgssed-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 ,solid tetrominoes" (r.jecting the row of four cubes and the ,,square,rof four 333 7 tl t tr4wtutufu& s Fie.47 , G A w U o