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Never underestimate the amazing ways that geometrical constructions can be made to fit together in space. Just when we think we have exhausted the possible hole arrangements for symmetrical hexagonal stick assemblies, yet another one is discovered. Note the arrangement of the four holes in the hexagonal stick shown in Fig. 134. If the hole at the bottom is ignored, the arrangement is helical; but if the hole at the top is ignored, the arrangement is alternate. Eight such identical sticks, together with their eight corresponding dowels, can be assembled into a structure having one fourfold axis of symmetry and four twofold axes - i.e. the same as that of a square prism. Furthermore, if four stick-dowel pairs are now joined to make elbow pieces, it becomes a most perplexing assembly puzzle. The elbow pieces have two possible forms, thus providing further amusement and bafflement for the determined puzzle analyst.
Fig. 134
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