  A violation of mirror symmetry in the $\eta\to\pi^+\pi^-\pi^0$ Dalitz plot
has long been recognized as a signal of C and CP violation. Here we show how
the isospin of the underlying C- and CP-violating structures can be
reconstructed from their kinematic representation in the Dalitz plot. Our
analysis of the most recent experimental data reveals, for the first time, that
the C- and CP-violating amplitude with total isospin $I=2$ is much more
severely suppressed than that with total isospin $I=0$.
