From the author’s introduction: We examine the structure of the set of primitive temporal relations in the framework defind by Allen. We show that this structure is conveniently described by a polygon which can be interpreted in three different ways. We then use this information to solve two problems: reducing the number of entries in Allen’s transition table, and determining a minimal set of primitive relations. We get - a simplified transitivity table, with only forty-three entries; a set of six primitive relations which, together with two involutions, generates the set of thirteen primitive relations.