ABSTRACT
Thirty Pentagonal Sticks and Dowels The cluster of 12 hexagonal sticks and dowels shown in Figure 142 has an analogy in 30 pentagonal sticks and dowels. The version shown in
Figure 165 has seven holes in each stick. A smaller version is possible using shorter sticks and dowels, with fi ve 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. The construction can be extended along any one axis and the structure will repeat itself in an indefi nite chain. It will not form a three-dimensional space-fi lling crystallographic lattice, however. In this game at least, no such constructions with fi vefold symmetries would appear to be possible. Pentagonal sticks are easy to make by fi rst ripping ¾-inch boards into trapezoidal sticks and then making two more cuts, all with the saw tilted 18 degrees (Figure 166). 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 fi le in an electric drill. Assembly is entertaining and not too diffi cult if aided by an illustration. Of course, the use of elbow pieces, as in the hexagonal counter-
part, would turn it into an exceedingly diffi cult puzzle. Instead, when this sculpture was produced in 1987-1988, it was as a straightforward construction kit with directions. One can spend hours studying the assembled structure, pondering its many mysterious properties and admiring its beautiful symmetries.
