Non-Hamiltonian simple 3-polytopes having just two types of faces

It is shown that for every value of an integer k, k?11, there exist 3-valent 3-connected planar graphs having just two types of faces, pentagons and k-gons, and which are non- Hamiltonian. Moreover, there exist ?=?(k) > 0, for these values of k, and sequences (G_n)^∞_n=1 of the said graphs for which V(G_n)→∞ and the size of a largest circuit of G_n is at most (1??)V(G_n); similar result for the size of a largest path in such graphs is established for all k, k?11, except possibly for k = 14, 17, 22 and k = 5m+ 5 for all m?2.