Summary: We consider the sublinear problem \[ \begin{cases} -\Delta u=| u|^{q-2}u\quad &\text{in }\Omega, \\ u_\nu=0\quad &\text{on }\partial\Omega,\end{cases} \] where \(\Omega\subset\mathbb R^N\) is a bounded domain, and \(1\leq q<2\). For \(q=1\), \(|u|^{q-2}u\) will be identified with \(\operatorname{sgn}(u)\). We establish a variational principle for least energy nodal solutions, and we investigate their qualitative properties. In particular, we show that they satisfy a unique continuation property (their zero set is Lebesgue-negligible). Moreover, if \(\Omega\) is radial, then least energy nodal solutions are foliated Schwarz symmetric, and they are nonradial in case \(\Omega\) is a ball. The case \(q=1\) requires special attention since the formally associated energy functional is not differentiable, and many arguments have to be adjusted.