  We report X-ray diffraction and magnetic susceptibility studies of the
structural phase transition in $\alpha$-RuCl$_{3}$. By utilizing a single
crystal sample with predominantly single twin domain, we show that
$\alpha$-RuCl$_{3}$ goes from high-temperature C2/m structure to a rhombohedral
structure with R$\bar{3}$ symmetry at low temperature. While the defining
feature of the structural transition is changing the stacking direction from
the monoclinic a-axis to the b-axis, bond-anisotropy disappears when the
structural change occurs, indicating that the local $C_3$ symmetry is restored
within the honeycomb layer. The symmetry change is corroborated by the
vanishing magnetic anisotropy in the low-temperature structure. Our study
demonstrates that magnetic interaction is extremely sensitive to structural
details in $\alpha$-RuCl$_{3}$, which could explain the sample dependence found
in this material.
