Biological systems exploit restricted degrees of freedom to drive self-assembly of nano- and microarchitectures. Simplified systems, such as colloidal nanoparticles that behave as lyotropic liquid crystalline mesophases in confined geometric spaces, may be used to mimic biological structures. Cellulose nanocrystals (CNCs) are colloidally stable nanoparticles that self-assemble into chiral nematic (ChN) liquid crystalline mesophases. To date, the self-assembly of ChN mesophases of CNCs has been studied under confinement conditions within curved surfaces or under drying conditions that impose curvatures that can be exploited to control ChN ordering; however, their self-assembly has not been investigated in geometries with square cross-sections under static conditions. Here, we show that because of surface anchoring on perpendicular surfaces, the ChN CNC phase is unable to bend with the 90° angle of the square capillary under increasing confinement. Instead, the ChN phase forms radial layers in the shape of concentric squircle shells. With increasing layer distance from the capillary wall, the squircles transition into concentric cylinder shells. In larger capillaries, the radial shell layers appear as a continuous spiral pattern that engulfs fragmented ChN pseudolayers, a defect to accommodate the cylindrical confinement of the mesophase. These results are useful for understanding the fundamentals of self-assembling systems and development of new technologies.