Multidomain samples of ferroics (ferroelectrics, ferroelastics, and
related materials) with fixed geometrical distribution of domains
can offer new macroscopic properties required for particular
applications. Two extreme cases of such applications are defined.
In domain-geometry-engineered samples of ferroic crystals, the
spatial distribution of domains and thus the spatial distribution of
tensorial properties is tuned to correspond to the k-vectors of
applied electric, optical or acoustic fields. For a given
wavelength, the size, geometry, and distribution of domains give
rise to a qualitatively new kind of response specified by the
symmetry of the multidomain system. In domain-average-engineered
samples of ferroic crystals, the specimen is subdivided into a very
large number of domains, representing µ domain states where µ is
smaller than the theoretically allowed maximum number, and forming a
regular or irregular pattern. Its response to external fields is
roughly described by tensorial properties averaged over all of the
domain states involved. The effective symmetry of the
domain-average-engineered system is given by a point group H and
we show how it can be determined. As an example, all groups H are
specified for domain-average-engineered samples which can arise in
a material undergoing the phase transition with symmetry change from
mm to 3m.