I'm trying to understand the topology behind a certain group which fits into a truncated crossed complex, so I've been trying to understand Brown's construction of the classifying space of a crossed complex. I asked a similar question here and the answer cleared up some of my misunderstanding.

What I'm looking for now is an explicit construction of such a space. I've not found any papers that give explicit examples of such a construction, but hopefully there is one somewhere. I'm looking for something along the lines of the easy to follow of the construction of the classifying space of cyclic groups.