The configuration of lines on a del Pezzo surface, such as
a cubic surface, leads to various root data, which lead in turn
to simple algebraic groups. After reviewing these constructions,
we show how to invert the process, by passing in a direct
geometrical way from the group to the surface.
This inverse construction, which is joint work with Grojnowski,
is motivated by boundary phenomena for moduli of K3 surfaces.