Spin measurement retrodiction revisited

The retrodiction of spin measurements along a set of different axes is revisited in detail. The problem is presented in two different pictures, a geometric and a general algebraic one. Explicit measurement operators that allow the retrodiction are given for the case of three and four axes. For the Vaidman-Aharanov-Albert case of three orthogonal axes the quantum network is constructed for two different initial Bell states.