type $\tilde A_2$ and $\tilde C_2$ with a uniform lattice in their full automorphism groups. The lattices act regularly, that is transitively and freely, on panels of the building having the same type. The advantages of this construction are very simple presentations for the lattices, very explicit descriptions of the buildings and a very good understanding how these lattices act on the building. Using the latter fact, we can calculate the group homology of the lattices. To the author’s knowledge, these are the first known presentations of lattices in buildings of type $\tilde C_2$.

It is known that there are countably many buildings of types $\tilde A_2$ and $\tilde C_2$ coming from algebraic groups over local fields, as well as uncountably many other so-called *exotic* buildings of these types. For the buildings of type $\tilde C_2$, all but possibly one of the buildings we construct are exotic. In the case of $\tilde A_2$, this is not known yet, except for a single building whose associated lattice we can realise explicitly in $\operatorname{SL}_3({\mathbb F}_2(\!(t)\!))$.

If the building $X$ we construct is classical, then there is an associated algebraic group $G\leq \operatorname{Aut}(X)$. By a result of Tits in [@Tit:BsT:74], the algebraic group 