Maximal Supersymmetry in Eleven-Dimensional Supergravity Revisited and   Chirotopes
  We analyze maximal supersymmetry in eleven-dimensional supergravity from the point of view of the oriented matroid theory. The mathematical key tools in our discussion are the Englert solution and the chirotope concept. We argue that chirotopes may provide other solutions not only for eleven-dimensional supergravity but for any higher dimensional supergravity theory. 
J. A. Nieto