Cubic harmonics are a mathematical generalization of spherical harmonics. While traditional spherical harmonics are used primarily in problems with spherical symmetry (like those in quantum mechanics, gravitation, and electromagnetism), cubic harmonics expand this concept to three-dimensional cubes or cubic geometries. In more technical terms, cubic harmonics can represent functions defined on a cube (or in cubic coordinates) much like how spherical harmonics represent functions defined on the surface of a sphere.
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