Monodisperse particles having: a single pure crystalline phase of a rare earth-containing lattice, a uniform three-dimensional size, and a uniform polyhedral morphology are disclosed. Due to their uniform size and shape, the monodisperse particles self assemble into superlattices. The particles may be luminescent particles such as down-converting phosphor particles and up-converting phosphors. The monodisperse particles of the invention have a rare earth-containing lattice which in one embodiment may be an yttrium-containing lattice or in another may be a lanthanide-containing lattice. The monodisperse particles may have different optical properties based on their composition, their size, and/or their morphology (or shape). Also disclosed is a combination of at least two types of monodisperse particles, where each type is a plurality of monodisperse particles having a single pure crystalline phase of a rare earth-containing lattice, a uniform three-dimensional size, and a uniform polyhedral morphology; and where the types of monodisperse particles differ from one another by composition, by size, or by morphology. In a preferred embodiment, the types of monodisperse particles have the same composition but different morphologies. Methods of making and methods of using the monodisperse particles are disclosed.