  The asynchronous capacity region of memoryless multiple-access channels is
the union of certain polytopes. It is well-known that vertices of such
polytopes may be approached via a technique called successive decoding. It is
also known that an extension of successive decoding applies to the dominant
face of such polytopes. The extension consists of forming groups of users in
such a way that users within a group are decoded jointly whereas groups are
decoded successively. This paper goes one step further. It is shown that
successive decoding extends to every face of the above mentioned polytopes. The
group composition as well as the decoding order for all rates on a face of
interest are obtained from a label assigned to that face. From the label one
can extract a number of structural properties, such as the dimension of the
corresponding face and whether or not two faces intersect. Expressions for the
the number of faces of any given dimension are also derived from the labels.
