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One way of overcoming the problem just explained is to space the sticks apart in the 12-piece burr, as shown in Fig. 74 on the left. Symmetry is maintained. The possibilities for notching combinations are virtually limitless. There is well-known variation of this with the sticks spaced farther apart so that it resembles a cage (Fig. 74 in the center). Sometimes a ball is placed inside. There is yet another variation, but non-homogeneous, with three more pairs of sticks added to fill the center spaces, even more complicated to design, to solve, or even to explain (Fig. 74 on the right).
Fig. 74
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