Factorization of cubic vertices involving three different higher spin fields

We derive a class of cubic interaction vertices for three higher spin fields, with integer spins ${\lambda }_1$, ${\lambda }_2$, ${\lambda }_3$, by closing commutators of the Poincar'e algebra in four-dimensional flat spacetime. We find that these vertices exhibit an interesting factorization property which allows us to identify off-shell perturbative relations between them.