Parallelism and Cubes inC2.c-Geometries

We characterizeC2.c-geometries that are truncations of almost-thinCn-geometries andC2.c-geometries covered by truncated almost-thin buildings of typeCn. 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 Brouwerʹs theorem is also given.