  By Birman and Skvortsov it is known that if $\Omegasf$ is a planar
curvilinear polygon with $n$ non-convex corners then the Laplace operator with
domain $H^2(\Omegasf)\cap H^1_0(\Omegasf)$ is a closed symmetric operator with
deficiency indices $(n,n)$. Here we provide a Kre\u\i n-type resolvent formula
for any self-adjoint extensions of such an operator, i.e. for the set of
self-adjoint non-Friedrichs Dirichlet Laplacians on $\Omegasf$, and show that
any element in this set is the norm resolvent limit of a suitable sequence of
Friedrichs-Dirichlet Laplacians with $n$ point interactions.
