Extending Locally Truncated Buildings and Chamber Systems

Suppose we are given a building, or more generally a flag-geometry, and we remove all vertices of certain specified types, together with the flags containing such vertices. This is called truncating the geometry; precise definitions and an extension of this concept to chamber systems are given in (1.5). Given some flag-geometry all of whose residues are isomorphic to those of a truncated geometry, it is reasonable to ask if it is itself a truncated geometry of the same type. Consider an example. The Sp8(2) building belongs to the following diagram