  A mathematical framework is developed to describe tilted perovskites using a
tensor description of octahedral deformations. The continuity of octahedral
tilts through the crystal is described using an operator which relates the
deformations of adjacent octahedra; examination of the properties of this
operator upon application of symmetry elements allows the space group of tilted
perovskites to be obtained. It is shown that the condition of octahedral
continuity across a planar defect such as an anti-phase boundary or domain wall
necessarily leads to different octahedral tilting at the defect, and a method
is given to predict the local tilt system which will occur in any given case.
Planar boundaries in the rhombohedral R3c a-a-a- tilt system are considered as
an example.
