Here's a practical instance of inconsistant orientation, which caused me some head-scratching at the time I first encountered it --- the algorithm employed for {\sl back face culling} of those faces of a convex polyhedron invisible at a given viewpoint when projected from {3-space} onto a given viewplane {2-space}. During the construction of the polyhedron from its vertex points, the polygons defining the faces all must be traversed in the same sense (say anticlockwise) when viewed from the exterior, for the purposes of computing face planes from vertices. The distances of faces visible at the viewpoint will then all have the same sign (say positive), and of faces invisible the opposite sign (say negative). However, visibility is a matter of P-orientation --- whether the external side of the plane is towards the viewer; but cyclic order of vertices is a matter of R-orientation --- whether an internal triangle is ordered anticlockwise. As a result, if the polyhedron becomes reflected in a plane mirror, it will also appear to the viewer to have mysteriously been turned inside out, unless the algorithm has been patched up by negating the distance signs. Fred Lunnon