  We study the generalized boundary value problem for (E)\; $-\Delta
u+|u|^{q-1}u=0$ in a dihedral domain $\Gw$, when $q>1$ is supercritical. The
value of the critical exponent can take only a finite number of values
depending on the geometry of $\Gw$. When $\gm$ is a bounded Borel measure in a
k-wedge, we give necessary and sufficient conditions in order it be the
boundary value of a solution of (E). We also give conditions which ensure that
a boundary compact subset is removable. These conditions are expressed in terms
of Bessel capacities $B_{s,q'}$ in $\BBR^{N-k}$ where $s$ depends on the
characteristics of the wedge. This allows us to describe the boundary trace of
a positive solution of (E)
