  A fullerene graph is a 3-connected cubic planar graph with pentagonal and
hexagonal faces. The leapfrog transformation of a planar graph produces the
trucation of the dual of the given graph. A fullerene graph is leapfrog if it
can be obtained from another fullerene graph by the leapfrog transformation. We
prove that leapfrog fullerene graphs on $n=12k-6$ vertices have at least
$2^{k}$ Hamilton cycles.
