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ABSTRACT Optical spectropolarimetry of the normal thermonuclear supernova (SN) 2019np from −14.5 to +14.5 d relative to B-band maximum detected an intrinsic continuum polarization (pcont) of 0.21 ± 0.09 per cent at the first epoch. Between days −11.5 and  +0.5, pcont remained ∼0 and by day +14.5 was again significant at 0.19 ± 0.10 per cent. Not considering the first epoch, the dominant axis of $${\rm Si\, {\small II}}$$ λ6355 was roughly constant staying close the continuum until both rotated in opposite directions on day  +14.5. Detailed radiation-hydrodynamical simulations produce a very steep density slope in the outermost ejecta so that the low first-epoch pcont ≈ 0.2 per cent nevertheless suggests a separate structure with an axis ratio ∼2 in the outer carbon-rich (3.5–4) × 10−3 M⊙. Large-amplitude fluctuations in the polarization profiles and a flocculent appearance of the polar diagram for the $${\rm Ca\, {\small II}}$$ near-infrared triplet (NIR3) may be related by a common origin. The temporal evolution of the polarization spectra agrees with an off-centre delayed detonation. The late-time increase in polarization and the possible change in position angle are also consistent with an aspherical 56Ni core. The pcont and the absorptions due to $${\rm Si\, {\small II}}$$ λ6355 and $${\rm Ca\, {\small II}}$$ NIR3 form in the same region of the extended photosphere, with an interplay between line occultation and thermalization producing p. Small-scale polarization features may be due to small-scale structures, but many could be related to atomic patterns of the quasi-continuum; they hardly have an equivalent in the total-flux spectra. We compare SN 2019np to other SNe and develop future objectives and strategies for SN Ia spectropolarimetry.