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Because of the millions of possible ways of dissecting the 4 x 4 x 4 cube into dissimilar, non-symmetrical, interlocking puzzle pieces, additional aesthetic considerations may be introduced to make the design process more of an art rather than just a series of random choices. The puzzle could be made serially interlocking, meaning that it can be assembled in one order only. Also, by using 1 x 1 x 2 blocks in the construction, symmetrical patterns can be realized on the six outside faces. Shown in Figs. 61a, 61b and 61c (made by Wayne Daniel) is a seven-piece dissection that attempts to achieve all of these. It was once produced as the Convolution Puzzle. It has one surprising step in assembly that requires a rotation, which is not possible unless certain edges are rounded ever so slightly. Can any reader devise a way to correct this mechanically slight but mathematically crippling deformity in an otherwise satisfactory design?
Fig. 61a
Fig. 61b
Fig. 61c
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