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The numbers of R-D blocks arranged in octahedral clusters are given by the following series: 6, 19, 44, 85, ... It is especially desirable that a dissection of the octahedral cluster be interlocking because it would fit so poorly into a box. There is a four-piece dissection of the 19-block octahedral cluster that is interlocking and assembles in one order only. All of the pieces are dissimilar and non-symmetrical. Three of them have five blocks and one piece has four blocks. Again, its discovery is left to the reader. The one known dissection shown in Fig. 172 may or may not be unique.
Fig. 172
The two interlocking R-D block puzzles above (Figs. 171 and 172) are both surprisingly difficult to solve. Even if the reader discovers the design by experimental dissection or some other method and makes a set of pieces, the solution has a way of vanishing from memory the moment the pieces are scrambled. Those made with spheres might be even more confusing.
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