A_2$ by Köhler, Meixner and Wester in [@KMW:A2l:84; @KMW:2ab:85] and by Kantor in [@Ka:SLF:87], all of these in characteristic two. All chamber-transitive lattices in classical buildings have been classified by Kantor, Liebler and Tits in [@KLT:CTL:87]. In particular, the examples of Köhler, Meixner, Wester and Kantor are the only $\tilde A_2$-buildings with chamber-transitive lattices.

Cartwright, Mantero, Steger and Zappa construct vertex-transitive lattices on buildings of type $\tilde A_2$ in [@CMSZ1; @CMSZ2]. They prove that some of the lattices they construct are contained in $\operatorname{SL}_3({\mathbb F}_q(\!(t)\!))$, while others correspond to exotic buildings.

In [@Ron:TG:84], Ronan constructs (possibly exotic) buildings of type $\tilde A_2$ admitting a lattice acting regularly on vertices of the same type.

Except for the single lattice which we can realise in $\operatorname{SL}_3({\mathbb F}_2(\!(t)\!))$, it is not clear whether any of our lattices are commensurable to the lattices constructed by Cartwright-Mantero-Steger-Zappa or by Ronan.

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For buildings of type $\tilde C_2$, there is a free construction by Ronan in [@Ron:CBR:86] which produces very unstructured examples of exotic buildings and does not give any control over the automorphism groups. In [@Kan:GPS:86], Kantor gives a construction of exotic buildings of type $\tilde C_2$ admitting uniform lattices acting freely on vertices of 