In -D 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).

**References**

Betke, U.; Henk, M.; and Wills, J. M. ``Finite and Infinite Packings.'' *J. Reine Angew. Math.* **453**, 165-191, 1994.

Betke, U. and Henk, M. ``Finite Packings of Spheres.'' *Discrete Comput. Geom.* **19**, 197-227, 1998.

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.

© 1996-9

1999-05-26