Extension of the platonic robustness theorem to downward robustness

In the setting of Theorem~, concerning robustness classes of convex solids and platonic solids, let downward external robustness and downward full robustness be the corresponding downward variants of external and full robustness. Extension of the platonic robustness theorem. Theorem~ is also valid for downward external robustness, and also for downward full robustness. This is posed as an open question in the discussion of robustness in three dimensions; the claim asks whether platonic solids have maximal downward full robustness in the platonic classes.