In n dimensions for n>=5 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 n-spheres. The conjecture was proposed by Fejes Tóth, and solved for dimensions >=42 by Betke et al. (1994) and Betke and Henk.

content | convex hull | hypersphere | hypersphere packing | sphere packing