  We study the problem of invisibility for bodies with a mirror surface in the
framework of geometrical optics. We show that for any two given directions it
is possible to construct a two-dimensional fractal body invisible in these
directions. Moreover, there exists a three-dimensional fractal body invisible
in three orthogonal directions. The work continues the previous study in [A.
Aleksenko and A. Plakhov. Bodies of zero resistance and bodies invisible in one
direction. Nonlinearity 22, 1247-1258 (2009)], [A Plakhov and V Roshchina.
Invisibility in billiards. Nonlinearity 24, 847-854 (2011)], where
two-dimensional bodies invisible in one direction and three-dimensional bodies
invisible in one and two orthogonal directions were constructed.
