  The Signorini problem for the Laplace operator is considered in a general
polygonal domain. It is proved that the coincidence set consists of a finite
number of boundary parts plus isolated points. The regularity of the solution
is described. In particular, we show that the leading singularity is in general
$r_i^{\pi/(2\alpha_i)}$ at transition points of Signorini to Dirichlet or
Neumann conditions but $r_i^{\pi/\alpha_i}$ at kinks of the Signorini boundary,
with $\alpha_i$ being the internal angle of the domain at these critical
points.
