  The angular part of the Faddeev equations is solved analytically for s-states
for two-body square-well potentials. The results are, still analytically,
generalized to arbitrary short-range potentials for both small and large
distances. We consider systems with three identical bosons, three non-identical
particles and two identical spin-1/2 fermions plus a third particle with
arbitrary spin. The angular wave functions are in general linear combinations
of trigonometric and exponential functions. The Efimov conditions are obtained
at large distances. General properties and applications to arbitrary potentials
are discussed. Gaussian potentials are used for illustrations. The results are
useful for numerical calculations, where for example large distances can be
treated analytically and matched to the numerical solutions at smaller
distances. The saving is substantial.
