5-regular 3-polytopal graphs with edges of only two types and shortness exponents less than one Original Research Article

It is shown that, if q ⩾ 29 and q ≢ 0 (mod 3), the infinite class of 5-regular 3-polytopal graphs whose edges are incident with either two triangles or a triangle and a q-gon contains nonhamiltonian members and even has shortness exponent less than one.