  We re-examine the constraints imposed by causality and unitarity on the
low-energy effective field theory expansion of four-particle scattering
amplitudes, exposing a hidden "totally positive" structure strikingly similar
to the positive geometries associated with grassmannians and amplituhedra. This
forces the infinite tower of higher-dimension operators to lie inside a new
geometry we call the "EFThedron". We initiate a systematic investigation of the
boundary structure of the EFThedron, giving infinitely many linear and
non-linear inequalities that must be satisfied by the EFT expansion in any
theory. We illustrate the EFThedron geometry and constraints in a wide variety
of examples, including new consistency conditions on the scattering amplitudes
of photons and gravitons in the real world.
