  The sixteen real coordinates of two-twistor space are transformed by a
nonlinear mapping into an enlarged space-time framework. The standard
relativistic phase space of coordinates $(X_\mu, P_\mu)$ is supplemented by a
six-parameter spin phase manifold (two pairs $(\eta_\alpha,\sigma_\alpha)$ and
$(\bar{\eta}_{\dot\alpha}, \bar{\sigma}_{\dot{\alpha}})$ of canonically
conjugated Weyl spinors constrained by two second class constraints) and the
electric charge phase space ($e,\phi$). The free two-twistor classical
mechanics is rewritten in this enlarged relativistic phase space as a model for
a relativistic particle. Definite values for the mass, spin and the electric
charge of the particle are introduced by means of three first class
constraints.
