The validity domain, within quantum mechanics, of a full set of eight
Bell inequalities for four observables is determined and represented g
eometrically. It turns out that the incorporation of all inequalities
increases considerably the domain of invalidity. For special spin cons
tellations, the validity regions become arbitrarily small. The results
are compared with experiment and used to elucidate the status of the
existing experimental evidence in favor of quantum theory and against
hidden variables.