  In this note we give a construction of a smooth Riemannian metric on R^n
which is standard Euclidean outside a compact set K and such that it has N =
n(n + 1)=2 invisible directions, meaning that all geodesics lines passing
through the set K in these directions remain the same straight lines on exit.
For example in the plane our construction gives three invisible directions.
This is in contrast with billiard type obstacles where a very sophisticated
example due to A.Plakhov and V.Roshchina gives 2 invisible directions in the
plane and 3 in the space. We use reflection group of the root system An in
order to make the directions of the roots invisible.
