A roof prism is in general any kind of reflective optical prism

Prism (optics)

In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

 containing a section where two faces meet at a 90° angle. Reflection from the two faces returns an image that is flipped laterally across the axis where the faces meet.

A single Porro prism

Porro prism

In optics, a Porro prism, named for its inventor Ignazio Porro, is a type of reflection prism used in optical instruments to alter the orientation of an image....

 is the simplest type of roof prism, though in its most common application (the double-Porro configuration in binoculars

Binoculars

Binoculars, field glasses or binocular telescopes are a pair of identical or mirror-symmetrical telescopes mounted side-by-side and aligned to point accurately in the same direction, allowing the viewer to use both eyes when viewing distant objects...

) it is not used as a roof prism.

Other common roof prisms are the Amici roof prism

Amici roof prism

An Amici roof prism, named for its inventor, the Italian astronomer Giovanni Amici, is a type of reflecting prism used to deviate a beam of light by 90° while simultaneously inverting the image...

, the Abbe–Koenig prism, the Schmidt–Pechan prism, and the roof pentaprism

Pentaprism

A pentaprism is a five-sided reflecting prism used to deviate a beam of light by 90°. The beam reflects inside the prism twice, allowing the transmission of an image through a right angle without inverting it as an ordinary right-angle prism or mirror would.The reflections inside the prism are not...

. (sources from: http://www.shawcreekbirdsupply.com/roof_porro_prisms.htm)