Spanning Point-line Geometries in Buildings of Spherical Type
We consider the point-line geometries that arise as a shadow space in a spherical building with a diagram of type An, Bn, Cn, Dn or En, and determine in which cases the geometry is spanned by the set of points on an apartment. It turns out that this happens precisely in the cases corresponding to a minimal weight.
Blok, Rieuwert J. and Brouwer, Andries E., "Spanning Point-line Geometries in Buildings of Spherical Type" (1998). Mathematics and Statistics Faculty Publications. 29.
Journal of Geometry