the set of normalized scalar products on ${\bf R}^n$ and a natural compactification consists in projectivizing the cone of positive nonzero semidefinite bilinear forms: what is done in [@Wer04] is the non-Archimedean analogue of this; it has some connection with Drinfeld spaces and is useful to our subsequent compactification in the vein of Satake’s work for symmetric spaces. The second way is related to representation theory [@Wer07]: it provides, for a given group, a finite family of compactifications of the Bruhat-Tits building. The compactifications, as in E. Landvogt’s monograph, are defined by gluing compactified Euclidean tilings but the variety of possibilities comes from exploiting various possibilities of compactifying equivariantly these tilings in connection with highest weight theory.

[**3.**]{} [*Use of Berkovich analytic geometry*]{}.—  The compactifications we would like to introduce here make a crucial use of Berkovich analytic geometry. There are actually two different ways to use the latter theory for compactifications.

The first way is already investigated by V. Berkovich himself when the algebraic group under consideration is split [@Ber1 Chap. 5]. One intermediate step for it consists in defining a map from the building to the analytic space attached to the algebraic group: this map attaches to each 