  The current understanding of spin-polarization phenomena in crystals relying
on the crystalline symmetries is far from complete. Here, we develop a
universal theory, consisting of five basic symmetry-constrained rules, to
capture the diverse spin textures (STs) in non-centrosymmetric crystals, via
exhaustively classifying the crystalline symmetry operations and their
combinations with time-reversal operation in symmetry-preserved k-invariant
subspace. Our theory is verified by extensive material examples based on the
first-principles calculations, explaining their kaleidoscopic STs or even
vanishing spin-polarization effect. Interestingly, based on our theory, we
argue that the generally accepted radial STs in chiral crystals cannot be
rigorous. More importantly, combining with topological band theory, we propose
the symmetry-constrained three-dimensional persistent STs, which is long sought
but never be discovered, could be abundant in two families of nonsymmorphic
crystals. Our theory could broaden our understanding of spin-polarization
effect and enable the dream of ab initio design of desirable STs in crystals.
