Relativistic velocity space, Wigner rotation and Thomas precession

We develop a relativistic velocity space called \emph{rapidity space} from the single assumption of Lorentz invariance, and use it to visualize and calculate effects resulting from the successive application of non-colinear Lorentz boosts. In particular, we show how rapidity space provides a geometric approach to Wigner rotation and Thomas precession in the same way that spacetime provides a geometrical approach to kinematic effects in special relativity.