Abstract
An n-cycle of balls is a cyclic sequence of non-overlapping n balls in R 3 in which each consecutive pair of balls are tangent. An (m,n)-link is a pair of an m-cycle and an n-cycle that form a non-splittable link, with no two balls overlapping. It is proved that (1) a (3,n)-link exists only when n ≥ 6, and in any (3,6)-link, each ball in the 3-cycle is tangent to all balls in the 6-cycle, (2) a (4,4)-cycle exists and in any (4,4)-cycle, each ball in a 4-cycle is tangent to all balls in the other 4-cycle.
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© 2000 Springer-Verlag Berlin Heidelberg
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Maehara, H., Oshiro, A. (2000). On Soddy’s Hexlet and a Linked 4-Pair. In: Akiyama, J., Kano, M., Urabe, M. (eds) Discrete and Computational Geometry. JCDCG 1998. Lecture Notes in Computer Science, vol 1763. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-46515-7_15
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DOI: https://doi.org/10.1007/978-3-540-46515-7_15
Publisher Name: Springer, Berlin, Heidelberg
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