  Massive spinning particle in $6d$-Minkowski space is described as a
mechanical system with the configuration space $R^{5,1} \times CP^3$. The
action functional of the model is unambiguously determined by the requirement
of identical (off-shell) conservation for the phase-space counterparts of three
Casimir operators of Poincar\'e group. The model proves to be completely
solvable. Its generalization to the constant curvature background is presented.
Canonical quantization of the theory leads to the relativistic wave equations
for the irreducible $6d$ fields.
