Simple 3-polytopal graphs with edges of only two types and shortness coefficients

Abstract We consider classes of simple 3-polytopal graphs whose edges are incident with either two 5-gons or a 5-gon and a q -gon ( q > 5). We show that the shortness coefficient is less than one for all q ⩾ 28, settle a question raised by Jendroľ and Tkac in a recent paper in the journal and prove that all the graphs in these classes are cyclically 4-edge-connected.