  We present D=3 and D=4 models for massive particles moving in a new type of
enlarged spacetime, with D-1 additional vector coordinates, which after
quantization lead to the towers of massive higher spin (HS) free fields. Two
classically equivalent formulations are presented: one with a hybrid
spacetime/bispinor geometry and a second described by a free two-twistor
dynamics with constraints. After quantization in the D=3 and D=4 cases, the
wave functions are given as functions on the SL(2,R) and SL(2,C) group
manifolds respectively, and describe arbitrary on-shell momenta and spin
degrees of freedom. Finally, the D=6 case and possible supersymmetric
extensions are mentioned.
