  The action dimension of a group G is the minimal dimension of a contractible
manifold that G acts on properly discontinuously. We show that if G acts
properly and cocompactly on a thick Euclidean building, then the action
dimension is bounded below by twice the dimension of the building. We also
compute the action dimension of S-arithmetic groups over number fields,
partially answering a question of Bestvina, Kapovich, and Kleiner.
