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Asymmetric interactions such as entropic (e.g., encoded by nonspherical shapes) or surface forces (e.g., encoded by patterned surface chemistry or DNA hybridization) provide access to functional states of colloidal matter, but versatile approaches for engineering asymmetric van der Waals interactions have the potential to expand further the palette of materials that can be assembled through such bottom-up processes. We show that polymerization of liquid crystal (LC) emulsions leads to compositionally homogeneous and spherical microparticles that encode van der Waals interactions with complex symmetries (e.g., quadrupolar and dipolar) that reflect the internal organization of the LC. Experiments performed using kinetically controlled probe colloid adsorption and complementary calculations support our conclusion that LC ordering can program van der Waals interactions by ~20 k B T across the surfaces of microparticles. Because diverse LC configurations can be engineered by confinement, these results provide fresh ideas for programming van der Waals interactions for assembly of soft matter.