The asynchronous capacity region of a memoryless multiple-access
channel is the union of certain polytopes henceforth called rate
regions. Each rate region has a dominant face and it is well-known
that vertices of the dominant face may be approached via a technique
called successive decoding. It is also known that an extension of
successive decoding applies to all points that are on the boundary of
the dominant face. The extension consists of forming groups of users
in such a way that users within a group can be decoded jointly whereas
groups are decoded successively. It is insightful to obtain these and 
new results as a straightforward consequence the structure of the rate 
regions. The focus of our presentation is on that structure. In particular, 
we show how an arbitrary face of a rate region decomposes into the Cartesian 
product of one or more lower-dimensional dominant faces and at most one rate region.