  We explore a Pluecker-type relation which occurs naturally in the study of
maximally supersymmetric solutions of certain supergravity theories. This
relation generalises at the same time the classical Pluecker relation and the
Jacobi identity for a metric Lie algebra and coincides with the Jacobi identity
of a metric n-Lie algebra. In low dimension we present evidence for a geometric
characterisation of the relation in terms of middle-dimensional orthogonal
planes in euclidean or lorentzian inner product spaces.
