  Unitarity identifies all power-law finite-volume effects and is, therefore,
the crucial S-matrix principle for a mapping between experimental results and
those of Lattice QCD calculations. In this contribution we review how 3-body
unitarity constrains the form of the 3-body scattering amplitude parametrized
by the tower of isobars. The result is discretized and projected to the
irreducible representations of the cubic group, leading to a fully relativistic
3-body quantization condition. The latter is used to deduce the finite-volume
excited level spectrum of the $\pi^+\pi^+\pi^+$ system, which agrees nicely
with the available lattice results by the NPLQCD collaboration.

High Energy Physics - Lattice