  We consider closed, Weyl-transitive groups of automorphisms of thick
buildings. For each element of such a group, we derive a combinatorial formula
for its scale and establish the existence of a tidy subgroup for it that equals
the stabilizer of a simplex. Simplices whose stabilizers are tidy for some
element of the group are characterized in terms of the minimal set of the
isometry induced by the element on the Davis-realisation of the building and in
terms of the Weyl-distance between them and their image. We use our results to
derive some topological properties of closed, Weyl-transitive groups of
automorphisms.
