In 
dimensions for 
the arrangement of hyperspheres whose convex
hull has minimal content is always a "sausage"
(a set of hyperspheres arranged with centers along
a line), independent of the number of 
-spheres. The conjecture was
proposed by Fejes Tóth, and solved for dimensions 
by Betke et al. (1994) and Betke and Henk (1998).
Sausage Conjecture
See also
Content, Convex Hull, Hypersphere, Hypersphere Packing, Sphere PackingExplore with Wolfram|Alpha
References
Betke, U. and Henk, M. "Finite Packings of Spheres." Discrete Comput. Geom. 19, 197-227, 1998.Betke, U.; Henk, M.; and Wills, J. M. "Finite and Infinite Packings." J. reine angew. Math. 453, 165-191, 1994.Croft, H. T.; Falconer, K. J.; and Guy, R. K. Problem D9 in Unsolved Problems in Geometry. New York: Springer-Verlag, 1991.Fejes Tóth, L. "Research Problems." Periodica Methematica Hungarica 6, 197-199, 1975.Referenced on Wolfram|Alpha
Sausage ConjectureCite this as:
Weisstein, Eric W. "Sausage Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SausageConjecture.html