In optical metamaterials, the scatterers are usually aligned symmetrically with respect to the unit cells of the
material. In this work, we consider metamaterials in which the "metamolecules" can be non-centrosymmetric
and have an arbitrary, but common, orientation in the unit cells. Such internally twisted crystalline structures
are difficult to find in natural materials, but metamaterials of this type can be designed and fabricated at will.
Here we present a theoretical method that enables a detailed analysis of internally twisted non-centrosymmetric
metamaterials. The method establishes a connection between the optical properties of a metamaterial and the
plane-wave optical response of a single two-dimensional array of metamolecules. In this theory, the effective
wave parameters, such as the refractive index and wave impedance, are retrieved. Using the model, we show that
these parameters can dramatically depend on the wave propagation direction and metamolecular orientation in
a metamaterial. This dependence provides a possibility to adjust and control the plane-wave content of optical
beams propagating in the material.