  We prove a regularity result for the Poisson problem $-\Delta u = f$, $u
|\_{\pa \PP} = g$ on a polyhedral domain $\PP \subset \RR^3$ using the \BK\
spaces $\Kond{m}{a}(\PP)$. These are weighted Sobolev spaces in which the
weight is given by the distance to the set of edges \cite{Babu70,
Kondratiev67}. In particular, we show that there is no loss of
$\Kond{m}{a}$--regularity for solutions of strongly elliptic systems with
smooth coefficients. We also establish a "trace theorem" for the restriction to
the boundary of the functions in $\Kond{m}{a}(\PP)$.
