Lowest Dimensional Portals to SU($N$) Exotics

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 $N$.