A cloaking device includes an object-side, an image-side and a cloaked region between the object-side and the image-side. An object-side polyhedron with an entrance side and an exit side parallel to the entrance side is positioned on the object-side and an image-side polyhedron with an entrance side and an exit side parallel to the entrance side is positioned on the image-side. The entrance side of the object-side polyhedron is oriented relative to a reference optical axis extending between the object-side and the image-side at an acute angle α and the exit side of the image-side polyhedron is oriented relative to the reference optical axis at an oblique angle equal to 180°−α. Light from an object positioned on the object-side of the cloaking device is redirected around the cloaked region, without total internal reflection of the light within the object-side polyhedron or the image-side polyhedron.