Shortness parameters for planar graphs with faces of only one type

We construct infinite sequences of non-Hamiltonian graphs and use them to show that the shortness exponent (or, in some cases, the shortness coefficient) is less than one for many classes of 3-connected planar graphs whose faces are all r-gons and whose vertices are all p-valent or q-valent, where p < q. Three of the five possible values of (r, p) are considered, namely (4.3). (3,3), and (3,4), in conjunction with most of the possible corresponding values of q.