# Explicit classifying spaces for crossed complexes

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.

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It depends what you need the construction for? How is your crossed complex arising precisely (and incidently what do you mean by the topology', will a simplicial model do)?
Suppose $G=<t|t^m>$. Then $BG$ can be constructed inductively cell by cell by killing off higher homotopy and taking limit of the resulting spaces. It's (mostly) clear that the result is an infinite dimensional lens space. I would be happy seeing any example where someone says, here is a crossed complex, here is the construction, and here is the classifying space. –  jd.r Jan 24 '10 at 23:58