image rotation prisms

From many kinds of prisms we can distinguish prisms that rotates input beam after few reflections inside. It means the output image is rotated about 180º with respect to input direction. Direction of the beam can be changed or unchanged.
Examples of image rotation prisms are:
ABBE-KOENIG prism is an image erector. It is set of prisms with roof faces for complete image reversal.
CORNER CUBE prism (Retroreflector ; TRIHEDRAL prism) In the corner cube prism three reflecting surfaces are erpendicular each to the other (like side walls of
the cube). The input surface is perpendicular to the cube diagonal. Disregarding the angle of incidence the output beam is parallel to the input one, but it is of opposite direction. In set of several corner prisms, for better matching, their entrance – exit surface is often hexagonal. In case of this prisms the phenomenon of full internal reflection occurs so it is not necessary, (however it is possible) to put mirror coating on the reflecting faces.
DOVE prism (Image Rotator) This prism rotates the image without changing the
direction of input beam, which is parallel to the hypotenuse. Rotation of the prisms in relation to the subject causes double rotation of the image. DOVE prism should be used in parallel beam.