at least.

[**2.**]{} [*Some compactification procedures*]{}.—  Compactifications of symmetric spaces were defined and used in the 60ies; they are related to the more difficult problem of compactifying locally symmetric spaces [@Satake2], to probability theory [@Furst], to harmonic analysis... One group-theoretic outcome is the geometric parametrization of classes of remarkable closed subgroups [@Moore]. For all the above reasons and according to the analogy between Bruhat-Tits buildings and symmetric spaces, it makes therefore sense to try to construct compactifications of Euclidean buildings.

When the building is a tree, its compactification is quite easy to describe [@SerreArbres]. In general, and for the kind of compactifications we consider here, the first construction is due to E. Landvogt [@La]: he uses there the fact that the construction of the Bruhat-Tits buildings themselves, at least at the beginning of Bruhat-Tits theory for the simplest cases, consists in defining a suitable gluing equivalence relation for infinitely many copies of a well-chosen Euclidean tiling. In Landvogt’s approach, the equivalence relation is extended so that it glues together infinitely many compactified copies of the Euclidean tiling used to construct the building. Another approach is more group-theoretic and relies on the analogy with symmetric spaces: since the symmetric space of 