  We study the group Tame($\mathbf A^3$) of tame automorphisms of the
3-dimensional affine space, over a field of characteristic zero. We recover, in
a unified and (hopefully) simplified way, previous results of Kuroda,
Shestakov, Umirbaev and Wright, about the theory of reduction and the relations
in Tame($\mathbf A^3$). The novelty in our presentation is the emphasis on a
simply connected 2-dimensional simplicial complex on which Tame($\mathbf A^3$)
acts by isometries.
