On a question of A. Koldobsky

We construct an example of a non-convex star-shaped origin-symmetric body D ⊂ R 3 such that its section function A D , ξ ( t ) : = area ( D ∩ { ξ ⊥ + t ξ } ) is decreasing in t ⩾ 0 for every fixed direction ξ ∈ S 2 .