  Inspired by the Bruhat-Tits building of SL$_n$($\mathbb Q_p$), we construct a
complete metric space X with an action of the tame automorphism group of the
affine space Tame($K^n$). The points in X are certain monomial valuations, and
X admits a natural structure of Euclidean CW-complex of dimension n-1. When n =
3, and for K of characteristic zero, we prove that X has non-positive curvature
and is simply connected, hence is a CAT(0) space. As an application we obtain
the linearizability of finite subgroups in Tame($K^3$).
