At high temperatures, microstructural evolution in polycrystalline materials is profoundly influenced by the grain boundary properties (energies, and mobilites) and their anisotropies. However, even for simple microstructures, the capability of representing the distributions of GB character, as a function of the five macroscopic degrees of freedom, has not been established. As the statistical distributions directly influence the interfacial network connectivity, developing a framework for quantifying GB distributions is a crucial missing step in the inverse-design of interface-dominated phenomena in polycrystalline systems. In this talk, I will present symmetrized functions, using the familiar hyperspherical harmonics, for representing grain boundary texture in the five-parameter space. The basis functions will also allow for the interpolation of structure-property relationships of grain boundaries, quantification of interfacial statistics in experimental microstructures.