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Using 2.93 fb−1 of 𝑒+𝑒− collision data taken at a center-of-mass energy of 3.773 GeV by the BESIII detector at the BEPCII, we measure the branching fractions of the singly Cabibbo-suppressed decays 𝐷→𝜔𝜋𝜋 to be ℬ(𝐷0→𝜔𝜋+𝜋−)=(1.33±0.16±0.12)×10−3 and ℬ(𝐷+→𝜔𝜋+𝜋0)=(3.87±0.83±0.25)×10−3, where the first uncertainties are statistical and the second ones systematic. The statistical significances are 12.9𝜎 and 7.7𝜎, respectively. The precision of ℬ(𝐷0→𝜔𝜋+𝜋−) is improved by a factor of 2.1 over prior measurements, and ℬ(𝐷+→𝜔𝜋+𝜋0) is measured for the first time. No significant signal for 𝐷0→𝜔𝜋0𝜋0 is observed, and the upper limit on the branching fraction is ℬ(𝐷0→𝜔𝜋0𝜋0)<1.10×10−3 at the 90% confidence level. The branching fractions of 𝐷→𝜂𝜋𝜋 are also measured and consistent with existing results.