 The polyhedral graphs are the graphs that are simultaneously planar and 3-vertex-connected; the assumption of 3-vertex-connectivity is necessary for these results, as there exist sets of 2-vertex-connected planar graphs (such as the complete bipartite graphs formula_13) with shortness exponent 0.There are many additional known results on shortness exponents of restricted subclasses of planar and polyhedral graphs.The 3-vertex-connected cubic graphs (without the restriction that they be planar) also have a shortness exponent that has been proven to lie strictly between 0 and 1.