Examples of buildings constructed via covering spaces

The purpose of this note is to use covering space theory to construct new examples of buildings. On the level of Coxeter systems, this contsruction was described previously in Davis [4]. It goes as follows. Start with a Coxeter system (W ′, S). Change some m(s, t)’s in its Coxeter matrix from integers ≥ 2 to the symbol ∞ . This defines a new Coxeter system (W, S). Suppose C′ is a building of type (W ′, S). We want to use it construct a building C of type (W, S). Let K be the “Davis chamber” for (W, S). Use it to get a realization U (C′,K) for C′ . Since we made changes in W ′ , the space U (C′,K) will not be simply connected. However, as we show in Theorem 2.5, its universal cover is the realization of a building C of type (W, S).