The Tóth Sausage Conjecture

The Tóth Sausage Conjecture is a project in Universal Paperclips. The conjecture states that in n dimensions for n≥5 the arrangement of n-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 László Fejes Tóth, and solved for dimensions n≥42 by Betke ''et al. ''(1994) and Betke and Henk (1998). It is unsolved in the general case.