  We find the combinations of momentum and domain-wall charges corresponding to
BPS states preserving 1/4, 1/2 or 3/4 of D=4 N=1 supersymmetry, and we show how
the supersymmetry algebra implies their stability. These states form the
boundary of the convex cone associated with the Jordan algebra of $4\times 4$
real symmetric matrices, and we explore some implications of the associated
geometry. For the Wess-Zumino model we derive the conditions for preservation
of 1/4 supersymmetry when one of two parallel domain-walls is rotated and in
addition show that this model does not admit any classical configurations with
3/4 supersymmetry. Our analysis also provides information about BPS states of
N=1 D=4 anti-de Sitter supersymmetry.
