We obtain a solution to eleven-dimensional supergravity that consists of
M2-branes embedded in a dielectric distribution of M5-branes. Contrary to
normal expectations, this solution has maximal supersymmetry for a brane
solution (i.e. sixteen supercharges). While the solution is constructed using
gauged supergravity in four dimensions, the complete eleven-dimensional
solution is given. In particular, we obtain the Killing spinors explicitly, and
we find that they are characterised by a duality rotation of the standard
Dirichlet projection matrix for M2-branes.Comment: 17 pages; harvma
