... − 1, are called the quads, hexes, respectively maxes, of ∆ The points and lines contained in a convex subspace of diameter δ ≥ define a dual polar space of rank δ In particular, the points and ... hyperplane of ∆, called the singular hyperplane of ∆ with deepest point x If A is a convex subspace of diameter δ of ∆ and HA is a hyperplane of A, then the set of points of ∆ at distance at most ... give an alternative description of these hyperplanes in terms of certain objects of the dual polar space, and in Section 2.3, we will prove that all these hyperplanes arise from the so-called Grassmann-embedding...