A new method is described for automatically reconstructing 3D planar faces from multiple images of a scene. The novelty of the approach lies in the use of inter-image homographies to validate and best estimate the plane, and in the minimal initialization requirements --- only a single 3D line with a textured neighbourhood is required to generate a plane hypothesis. The planar facets enable line grouping and also the construction of parts of the wireframe which were missed due to the inevitable shortcomings of feature detection and matching.The method allows a piecewise planar model of a scene to be built completely automatically, with no user intervention at any stage, given only the images and camera projection matrices as input. The robustness and reliability of the method are illustrated on several examples, from both aerial and interior views.