Parallelism and Cubes inC2.c-Geometries

Abstract

We characterize C 2 .c-geometries that are truncations of almost-thin C n -geometries and C 2 .c-geometries covered by truncated almost-thin buildings of type C n . Then we show how to profit from those characterizations in the investigation of a number of special cases. The proof of our main theorem is a rearrangement of the proof of a theorem by Brouwer on rectagraphs. A generalization of Brouwer's theorem is also given.