A study of $CP$ violation in $B^{\mp }\to D{h}^{\mp }$ ($h=K,\pi$) with the modes $D\to K^{\mp }{\pi }^{\pm }{\pi }^0$, $D\to {\pi }^{+}{\pi }^{-}{\pi }^0$ and $D\to K^{+}{K}^{-}{\pi }^0$

An analysis of the decays of $B^{\mp }\to D{K}^{\mp }$ and $B^\mp \rightarrow D \pi^\mp $ispresentedinwhichthe$D$ meson is reconstructed in the three-body final states $K^{\mp }{\pi }^{\pm }{\pi }^0$, ${\pi }^{+}{\pi }^{-}{\pi }^0$ and $K^+ K^- \pi^0$. Using data from LHCb corresponding to an integrated luminosity of 3.0 fb${}^{-1}$ of $pp$ collisions, measurements of several $CP$ observables are performed. First observations are obtained of the suppressed ADS decay $B^\mp \rightarrow [\pi^\mp K^\pm \pi^0]_D \pi^\mp$andthequasi-GLWdecay$B^\mp \rightarrow [K^+ K^- \pi^0]_D \pi^\mp$. The results are interpreted in the context of the unitarity triangle angle $\gamma$ and related parameters.