The balcony of a continuator is defined as its points that are not covered by any other maximal square (see figure).

No square can be both a continuator and a separator. In general polygons, there may be squares that are neither continuators nor separators, but in simple polygons this cannot happen:
# In a simple rectilinear polygon, every maximal square is either a separator or a continuator. This is also true for rectangles: every maximal rectangle is either a separator or a continuator.
# In a simple rectilinear polygon