  Trapezoidal words are finite words having at most n+1 distinct factors of
length n, for every n>=0. They encompass finite Sturmian words. We distinguish
trapezoidal words into two disjoint subsets: open and closed trapezoidal words.
A trapezoidal word is closed if its longest repeated prefix has exactly two
occurrences in the word, the second one being a suffix of the word. Otherwise
it is open. We show that open trapezoidal words are all primitive and that
closed trapezoidal words are all Sturmian. We then show that trapezoidal
palindromes are closed (and therefore Sturmian). This allows us to characterize
the special factors of Sturmian palindromes. We end with several open problems.
