= Solution
A <polar liquid crystal> distinguishes the two ends of each constituent. Its orientational order is described by a vector $\mathbf p$, and $\mathbf p$ and $-\mathbf p$ represent different states. A <nematic liquid crystal> has head-tail symmetry, so its director obeys $\mathbf n\sim-\mathbf n$. Its lowest-rank faithful <nematic order parameter> is the symmetric traceless tensor
$$
Q_{ij}=S\left(n_in_j-\frac13\delta_{ij}\right),
$$
which is unchanged by $\mathbf n\mapsto-\mathbf n$.
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