Slices of L. Fejes Tóth's sausage conjecture

Let be k non-overlapping translates of the unit d -ball B d in euclidean d -space E d . Let C k denote the convex hull of their centres and let S k be a segment of length 2( k – 1). Furthermore, let V d denote the d -volume. L. Fejes Toth conjectured in [1], that, for d ≥ 5,