Wikipedia
A roof prism (also called a Dach prism or Dachkanten prism, from the German: "Dachkante", lit. roof edge) is a reflective optical prism containing a section where two faces meet at a 90° angle. These two 90° faces resemble the roof of a building, giving this prism type its name. Reflection from the two 90° faces returns an image that is flipped laterally across the axis where the faces meet.
Characteristic for a roof prism is that the beam is split in half, with one half of the beam hitting first one face then the other face, while it is invert for the other half of the beam. Therefore, a roof prism can be used only with some distance to focal planes, or the "edge" of the roof would introduce slight distortions. Furthermore, the angle between the two faces has to be very close to 90°, or image quality would be degraded.
The simplest roof prism is the Amici roof prism, with other common roof prism designs being the Abbe–Koenig prism, the Schmidt–Pechan prism and probably the best known being the roof pentaprism pictured here. A porro prism is not a roof prism, contrary to popular notion, as the two 90° faces usually don't meet in a Porro prism and therefore don't form a roof edge.