Normality conjecture for three-dimensional cyclic polytopes

A cyclic polytope is the convex hull of points on the moment curve; here, normal means that every lattice point in every positive dilate is a sum of lattice points of the polytope. Normality conjecture. All cyclic polytopes of dimension $3$ are normal. This is presented as a conjecture based on exhaustive computational experience; normality is automatic in dimension $2$, while the dimension-$3$ case remains open in the source.