  There is an elementary but indispensable relationship between the topology
and geometry of massive particles. The geometric spin $s$ is related to the
topological dimension of the internal space $V$ by $\dim V = 2s + 1$. This
breaks down for massless particles, which are characterized by their helicity
$h$, but all have 1D internal spaces. We show that a subtler relation exists
between the topological and geometry of massless particles. Wave functions of
massless particles are sections of nontrivial line bundles over the lightcone
whose topology are completely characterized by their first Chern number $C$. We
prove that in general $C = -2h$. In doing so, we also exhibit a method of
generating all massless bundle representations via an abelian group structure
of massless particles.
