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Among the various ways that uniform spheres can be packed in space, they show a natural inclination to arrange themselves most densely the same way that rhombic dodecahedra pack. Thus, in the Leftover Block Puzzle or almost any other, spheres might be substituted for rhombic dodecahedra. One advantage of spheres is that they are readily available in toy stores and educational supply shops, and usually quite accurate. The disadvantage is that they are more difficult to join together strongly. They can be bonded with epoxy, but an even better way with wooden balls is to drill holes and use dowelled joints.
The substitution of spheres for rhombic dodecahedra is not exactly equivalent mathematically. Spheres have an additional symmetry that the rhombic dodecahedra lack. This is demonstrated by the mirror-image pair of R-D pieces shown in Fig. 170, both of which have the same spherical counterpart. Thus, pieces made with spheres will generally produce more solutions and construct more figures, which could be an advantage or disadvantage depending upon the circumstances. Spherical versions also tend to fall apart more easily, so the pyramidal constructions may require a retaining base.
Fig. 170
Of course, spheres might also be substituted anywhere that cubes are used. But like playing billiards with elliptical balls, one should ask not if it is possible but rather if it is practical!
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