  Started from our work "Fields on the Poincare Group and Quantum Description
of Orientable Objects" (EPJC,2009), we consider here a classification of
orientable relativistic quantum objects in 3+1 dimensions. In such a
classification, one uses a maximal set of 10 commuting operators (generators of
left and right transformations) in the space of functions on the Poincare
group. In addition to usual 6 quantum numbers related to external symmetries
(given by left generators), there appear additional quantum numbers related to
internal symmetries (given by right generators). We believe that the proposed
approach can be useful for description of elementary spinning particles
considering as orientable objects. In particular, their classification in the
framework of the approach under consideration reproduces the usual
classification but is more comprehensive. This allows one to give a
group-theoretical interpretation to some facts of the existing phenomenological
classification of known spinning particles.
