  Equivariant Ehrhart theory generalizes the study of lattice point enumeration
to also account for the symmetries of a polytope under a linear group action.
We present a catalogue of techniques with applications in this field, including
zonotopal decompositions, symmetric triangulations, combinatorial
interpretation of the $h^\ast$-polynomial, and certificates for the
(non)existence of invariant non-degenerate hypersurfaces. We apply these
methods to several families of examples including hypersimplices, orbit
polytopes, and graphic zonotopes, expanding the library of polytopes for which
their equivariant Ehrhart theory is known.
