Quaternion neural networks (QNNs) form a class of neural networks constructed with quaternion numbers. They are suitable for processing 3-D features with fewer trainable free parameters than real-valued neural networks (RVNNs). This article proposes symbol detection in wireless polarization-shift-keying (PolSK) communications by employing QNNs. We demonstrate that quaternion plays a crucial role in the symbol detection of PolSK signals. Existing artificial-intelligence communication studies mainly focus on RVNN-based symbol detection in digital modulations having constellations in complex plane. However, in PolSK, information symbols are represented as the state of polarization, which can be mapped on the Poincare sphere and thus its symbols have a 3-D data structure. Quaternion algebra offers a unified representation to process 3-D data with rotational invariance and, therefore, it keeps the internal relationship among three components of a PolSK symbol. Hence, we can expect that QNNs learn the distribution of received symbols on the Poincare sphere with higher consistency to detect the transmitted symbols more efficiently than RVNNs. We compare PolSK symbol detection accuracy of two types of QNNs, RVNN, existing methods such as least-square and minimum-mean-square-error channel estimations, as well as detection knowing perfect channel state information (CSI). Simulation results including symbol error rate show that the proposed QNNs outperform the existing estimation methods and that they reach better results with two to three times fewer free parameters than the RVNN. We find that QNN processing will bring practical use of PolSK communications.