The surface of many modern structures such as the Louvre pyramid shown here consist of planes (faces), lines (edges) and points (corners, vertices). In projective 3-space there is an interesting duality between points and planes, lines and lines. Thus two points determine a line, two planes determine a line. Again, three points not on the same line determine a plane, three planes not through the same line determine a point. This pretty duality fails with Euclidean geometry because two planes may be parallel; such behaviour is disallowed in projective geometry! What happens with points and lines in the (projective) plane?
