Deza and Grishukhin studied \(3\)-valent maps \(M_n{(p,q)}\) consisting of a ring of \(n\) \(g\)-gons whose inner and outer domains are filled by \(p\)-gons. They described the conditions for \(n, p, q\) under which such a map may exist and presented several infinite families of them. We extend their results by presenting several new maps concerning mainly large values of \(n\) and \(q\).