Partial differential equations that are invariant under
Euclidean transformations are traditionally used as models in
pattern formation. These models are often posed on finite
domains (in particulary, multidimensional rectangles). Defining
the correct boundary conditions is often a very subtle problem.
On the other hand, there is pressure to choose boundary
conditions which are attractive to mathematical treatment.
Geometrical shapes and mathematically friendly boundary
conditions usualy imply spatial symmetry. The presence of
symmetry effects that are "hidden" in the boundary conditions
was noticed and carefully investigated by several researchers
during the past 15-20 years. Here we review developments in
this subject and introduce a unifying formalism to uncover
spatial hidden symmetries (hidden translations and
hidden rotations) in multidimensional rectangular domains with
Neumann boundary conditions.