The following problem was raised by Kuperberg [10]. What is the maximum number of infinite unit cylinders in E3 that can touch a unit ball without overlapping each other? It is conjectured that the number is 6, but observe that the configuration of six unit cylinders touching a unit ball is not unique. It was shown in [7] that the number in question is not greater than 8. In this paper we will consider the "dual" of this problem.
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