  Originally introduced and studied by the third and fourth authors together
with J. Justin and S. Widmer in arXiv:0801.1656, rich words constitute a new
class of finite and infinite words characterized by containing the maximal
number of distinct palindromes. Several characterizations of rich words have
already been established. A particularly nice characteristic property is that
all 'complete returns' to palindromes are palindromes. In this note, we prove
that rich words are also characterized by the property that each factor is
uniquely determined by its longest palindromic prefix and its longest
palindromic suffix.
