Abstract
In this note we prove an upper bound of seven for the maximum number of unit cylinders touching a unit ball in a packing. This improves a previous bound of eight by Heppers and Szab. The value conjectured by Kuperberg in 1990 is six.
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Fichtenholz, G. M.: Differential-und Integralrechnung III, VEB Deutscher Verlag der Wissenschaften, Berlin, 1974.
Graf, C. and Paukowitsch, P.: Möglichst dichte Packungen aus kongruenten Drehzylindern mit paarweise windschiefen Achsen, Elem. Math. 52 (1997) 71–83.
Heppes, A. and Szabó, L.: On the number of cylinders touching a ball, Geom. Dedicata 40 (1991), 111–116.
Kuperberg, K.: A nonparallel cylinder packing with positive density, Mathematika 37 (1990), 324–331.
Kuperberg, W.: Problem 3.3, DIMACS report on Workshop on Polytopes and Convex Sets, Rutgers University 1990.
Szabó, L.: On the density of unit balls touching a unit cylinder, Arch. Math. 64 (1995), 459–464.
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Braß, P., Wenk, C. On the Number of Cylinders Touching a Ball. Geometriae Dedicata 81, 281–284 (2000). https://doi.org/10.1023/A:1005290809501
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DOI: https://doi.org/10.1023/A:1005290809501