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The cluster of 12 hexagonal sticks and dowels shown in Fig. 128 has an analogy in 30 pentagonal sticks and dowels. The version shown in Fig. 152 has seven holes in each stick. A smaller version is possible using shorter sticks and dowels, with five holes in each stick; while yet another smaller and more spherical version has only three holes in each stick. There is also one larger and more stellated version with nine holes in each stick.
Fig. 152
The construction can be extended along any one axis and the structure will repeat itself in an indefinite chain. It will not form a three-dimensional space-filling crystallographic lattice, however - none are possible having fivefold symmetries.
Pentagonal sticks are easy to make by first ripping ¾-inch boards into trapezoidal sticks and then making two more cuts, all with the saw tilted 18 degrees (Fig. 153). All of the holes are drilled at an angle of 63½ degrees to the axis of the stick, passing through the center of the stick, and parallel to one face. Determining their irregular spacing is the tricky part. It could be calculated, but the author must confess he found it simpler to locate them by trial and error. Slight inaccuracies in the 210 holes can be corrected by reaming them through in the assembled or partially assembled state using a round file in an electric drill.
Fig. 153
Assembly is entertaining and not too difficult if aided by an illustration. Of course, the use of elbow pieces as in the hexagonal counterpart would turn it into an exceedingly difficult puzzle. One can spend hours studying the assembled structure, pondering its many mysterious properties and admiring its beautiful symmetries.
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