Crystallographic space group symmetry (CPGS) such as polar and nonpolar crystal classes have long been known to classify compounds that have spin-orbit-induced spin splitting. While taking a journey through the Brillouin Zone (BZ) from one k-point to another for a fixed CPGS, it is 
expected that the wavevector point group symmetry (WPGS) can change, and consequently a qualitative change in the texture of the spin polarization (the expectation value of spin operator S ⃗_(nk_0 ) in Bloch state u(n,k) and the wavevector k_0). However, the nature of the spin texture (ST) change is generally unsuspected. In this work, we determine a full classification of the linear-in-k spin texture patterns based on the polarity and chirality reflected in the WPGS at k_0. The spin-polarization vector S ⃗_(nk_0 ) controlling the ST is bound to be parallel to the rotation axis and perpendicular to the mirror planes and hence, symmetry operation types in WPGSs impose symmetry restriction to the ST. For instance, the ST is always parallel to the wavevector k in non-polar chiral WPGSs since they contain only rotational symmetries. Some consequences of the ST classification based on the symmetry operations in the WPGS include the observation of ST patterns that are unexpected according to the symmetry he crystal. For example, it is usually established that spin-momentum locking effect (spin vector always perpendicular to the wavevector) requires the crystal inversion symmetry breaking by an asymmetric electric potential. However, we find that polar WPGS can have this effect even in compounds without electric dipoles or external electric fields. We use the determined relation between WPGS and ST as a design principle to select compounds with multiple ST near band edges at different k-valleys. Based on high-throughput calculations for 1481 compounds, we find 37 previously fabricated materials with different ST near band edges.