  Tree-level scattering amplitudes of particles have a geometrical description
in terms of intersection numbers of pairs of twisted differential forms on the
moduli space of Riemann spheres with punctures. We customize a catalog of
twisted differential forms containing both already known and new differential
forms. By pairing elements from this list intersection numbers of various
theories can be furnished to compute their scattering amplitudes. Some of the
latter are familiar through their CHY description, but others are unknown.
Likewise, certain pairings give rise to various known and novel double-copy
constructions of spin-two theories. This way we find double copy constructions
for many theories, including higher derivative gravity, (partial massless)
bimetric gravity and some more exotic theories. Furthermore, we present a
derivation of amplitude relations in intersection theory.
