  We consider Weyl symmetric structure of the classical vacuum in quantum
chromodynamics. In the framework of formalism of gauge invariant Abelian
projection we show that classical vacuums can be constructed in terms of
Killing vector fields on the group SU(3). Consequently, homotopic classes of
Killing vector fields determine the topological structure of the vacuum. In
particular, the second homotopy group \pi_2(SU(3)/U(1)\times U(1)) describes
all topologically non-equivalent vacuums which are classified by two
topological numbers. For each given Killing vector field one can construct six
vacuums forming Weyl sextet representation. An interesting feature of SU(3)
gauge theory is that it admits a Weyl symmetric vacuum represented by a linear
superposition of the six vacuums from the Weyl vacuum sextet. A non-trivial
manifestation of Weyl symmetry is demonstrated on monopole solutions. We
construct a family of finite energy monopole solutions in Yang-Mills-Higgs
theory which includes Weyl monopole sextet. From the analysis of the classical
vacuum structure and monopole solutions we conjecture that a similar Weyl
symmetric vacuum structure can be realized in quantum theory.
