We demonstrate that the energy transport of surface phonon polaritons can efficiently be observed in a crystal made up of a three-dimensional assembly of spheroidal nanoparticles of silicon carbide. The ultralow phonon thermal conductivity of this nanostructure, along with its high surface area-to-volume ratio, allows the predominance of the polariton energy over that generated by phonons. The polariton dispersion relation, propagation length, and thermal conductance are numerically determined as functions of the size, shape, and temperature of the nanoparticles. It is shown that the thermal conductance of a crystal with prolate nanoparticles at 500 K and a minor (major) axis of 50 nm (5μm) is 0.5nWK-1, which is comparable to the quantum of thermal conductance of polar nanowires. We also show that a nanoparticle size dispersion of up to 200 nm does not change significantly the polariton energy, which supports the technological feasibility of the proposed crystal.