Moufang Polygons

1 Buildings Let Π be a Coxeter diagram with vertex set I and let W be the corresponding Coxeter group. Thus W is a group generated by the set I subject to relations which can be read off from the labels on the edges of Π. Let ∆ be a building of type Π. For these notes, it suffices to consider ∆ as a graph whose vertices are the chambers, where two chambers are joined by an edge whenever they lie in a common panel. If the type of a panel P (viewed as a simplex) is I\{i}, we give each edge joining two chambers of P the ”color” i.