  We study the massless irreducible representations of the Poincar\'{e} group
in the six-dimensional Minkowski space. The Casimir operators are constructed
and their eigenvalues are found. It is shown that the finite spin (helicity)
representation is defined by two integer or half-integer numbers while the
infinite spin representation is defined by the real parameter $\mu^2$ and one
integer or half-integer number.
