Non-hamiltonian 54-tough maximal planar graphs

By a theorem of Whitney (1931) the toughness t(G) of a non-hamiltonian maximal planar graph G is less than or equal to 32. Improving a result of Dillencourt (1991), it is shown that the shortness exponent of the class of maximal planar graphs with toughness greater than or equal to 54 is less than 1.