  New matter fields charged under the strong nuclear force would have dramatic
phenomenological implications. Here, we systematically explore how these new
states, which we postulate belong to some representation of SU(3) of quantum
chromo-dynamics, could interact with Standard Model fields: We analyze all
lowest-dimensional "portal" operators for any SU(3) representation and,
motivated by grand unification, we extend our results to SU($N$), for $N>3$. We
provide a publicly available python code, "tessellation", that automatically
constructs said lowest-dimensional portal operators for any new exotic matter
field charged under SU($N$) for any $N$.
