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The decay τ-→2π-π+3π0ντ has been studied with the CLEO II detector at the Cornell Electron Storage Ring. The branching fraction is measured to be (2.85 ± 0.56 ± 0.51) X 10-4. The result is in good agreement with the isospin expectation but somewhat below the conserved-vectorcurrent prediction. We have searched for resonance substructure in the decay. Within the statistical precision, the decay is saturated by the channels τ-→π-2π0ωντ, 2π-π+ωντ, and π-2π0ωντ This is the first observation of this ω decay mode and the branching fraction is measured to be (1.89-0.67+0.74 ± 0.40) X 10-4.