Reef squids belong to a group reputed for polarization sensitivity, yet polarization patterns of reef squid have not been quantified in situ. To quantify polarization patterns from video polarimetric data, we developed a protocol to map two-dimensional polarization data onto squid-shaped three-dimensional tessellated surfaces. This protocol provided a robust data container used to investigate three-dimensional regions-of-interest, producing data lineouts derived from the squid's geometry. This protocol also extracted polarimeter and squid body orientations and the solar heading from polarization images. When averaged over the solar heading, the ventral midline gave a low degree of polarization (2.4 ± 5.3%), and the area between the ventral and flank midlines had higher values (9.0 ± 5.3%). These averaged data had a large discontinuity in the angle of polarization (AoP) at the mantle's ventral midline (64 ± 55°), with larger discontinuities measured on individual squid. Ray-tracing calculations demonstrated that the AoP pattern was not related to the squid's surface-normal geometry. However, the AoP followed virtual striation axes on the squid's surface oriented 24° to the squid's long axis, similar in angle (27°) to the striations of birefringent collagen fibres documented in other squid species' skin.