The invention relates to an external composite housing for a compressor of an axial turbomachine, the housing having a generally circular wall with a matrix and fiber reinforcement. The housing includes a circular wall with an internal surface having a continuous curve around the circumference of the wall. The wall includes flat facets that are flush with the internal curved surface of the wall. The facets are arranged in annular rows to receive annular rows of stator vanes. The facets are flat disks against which the vanes bear to optimize the orientation of the vanes, while reducing the concentrations of mechanical stresses at the platform/wall interfaces.