Heights of minor faces in triangle-free 3-polytopes

The height h(f) of a face f in a 3-polytope is the maximum of the degrees of vertices incident with f. A 4-face is pyramidal if it is incident with at least three 3-vertices. We note that in the (3, 3, 3, n)-Archimedean solid each face f is pyramidal and satisfies h(f) = n.