  The charmless three-body decay modes $B^{\pm} \rightarrow K^{\pm} \pi^{+}
\pi^{-}$, $B^{\pm} \rightarrow K^{\pm} K^{+} K^{-}$, $B^{\pm} \rightarrow
\pi^{\pm} K^{+} K^{-}$ and $B^{\pm} \rightarrow \pi^{\pm} \pi^{+} \pi^{-}$ are
reconstructed using data, corresponding to an integrated luminosity of
3.0\;$\mbox{\,fb}^{-1}$, collected by the LHCb detector. The inclusive $C\!P$
asymmetries of these modes are measured to be $$ A_{C\!P}(B^{\pm} \rightarrow
K^{\pm} \pi^{+} \pi^{-})= +0.025 \pm 0.004 \pm 0.004 \pm 0.007 \\
A_{C\!P}(B^{\pm} \rightarrow K^{\pm} K^{+} K^{-}) = -0.036 \pm 0.004 \pm 0.002
\pm 0.007 \\ A_{C\!P}(B^{\pm} \rightarrow \pi^{\pm} \pi^{+} \pi^{-})= +0.058
\pm 0.008 \pm 0.009 \pm 0.007 \\ A_{C\!P}(B^{\pm} \rightarrow \pi^{\pm} K^{+}
K^{-})= -0.123 \pm 0.017 \pm 0.012 \pm 0.007 $$ %% where the first uncertainty
is statistical, the second systematic, and the third is due to the $C\!P$
asymmetry of the $B^{\pm} \rightarrow J/\psi K^{\pm}$ reference mode. The
distributions of these asymmetries are also studied as functions of position in
the Dalitz plot and suggest contributions from rescattering and resonance
interference processes.
