Non-discrete Euclidean buildings for the Ree and Suzuki groups

We call a non-discrete Euclidean building a {\it Bruhat-Tits space} if its automorphism group contains a subgroup that induces the subgroup generated by all the root groups of a root datum of the building at infinity. This is the class of non-discrete Euclidean buildings introduced and studied by Bruhat and Tits. We give the complete classification of Bruhat-Tits spaces whose building at infinity is the fixed point set of a polarity of an ambient building of type $\hbox{\sf B}_2$, $\hbox{\sf F}_4$ or $\hbox{\sf G}_2$ associated with a Ree or Suzuki group endowed with the usual root datum. (In the $\hbox{\sf B}_2$ and $\hbox{\sf G}_2$ cases, this fixed point set is a building of rank one; in the $\hbox{\sf F}_4$ case, it is a generalized octagon whose Weyl group is not crystallographic.) We also show that each of these Bruhat-Tits spaces has a natural embedding in the unique Bruhat-Tits space whose building at infinity is the corresponding ambient building.