  The computational cost of micromechanics for heterogeneous materials can be
reduced in certain cases where symmetric boundary conditions are applicable. We
derived an eighth symmetric formulation of the Generalized Method of Cells for
triply periodic microstructures. During this endeavor, an inherent symmetry was
discovered. This implied that all repeating unit cells may be quarter symmetric
representations of other microstructures. Additionally, it was discovered that
a repeating unit cell can have columns of subcells swapped with no changes to
the local or global fields. We concluded that first-order micromechanics are
not well suited for capturing detailed or complex microstructures; however,
higher-order theories, such as High Fidelity Generalized Method of Cells, can
adequately model these microstructures.
