Typical Faces and Weighted Faces

A natural way to associate an ‘average’ cell with a nondegenerate stationary Poisson hyperplane tessellation is that of defining the typical cell. Simpler is the definition of the zero cell. The zero cell can be viewed, if translations are ignored, as the volume-weighted version of the typical cell. For \(k\in \{0,\dots ,d\}\) , we have already defined typical k-faces. In this chapter, we introduce and study also weighted typical k-faces. Thus, we extend some of the relations between typical cells and weighted typical cells to lower-dimensional faces. But the study of faces in general has new aspects. One reason for this is that a proper face of positive dimension has a direction, and conditions involving a direction as well as distributions of directions are of interest. The consideration of more general weights for faces also allows us to draw conclusions about second moments for typical faces.