The paper is concerned with geometric properties of Coxeter matroids. A Coxeter matroid, also called WP-matroid, is a subset \(M\) of the set of cosets \(W/P\) of a Coxeter group \(W\) modulo a parabolic subgroup \(P\) such that \(M\) satisfies a certain maximality condition. More precisely, for each \(w\in W\) there is an element \(x\in M\) such that for all \(y\in M\) the element \(w^{-1}y\) precedes or equals \(w^{-1}x\) in the strong Bruhat order. The first main result of the paper provides an equivalent geometric version of this algebraic definition of a Coxeter matroid \(M\). For that \(M\) is interpreted as the set of faces of the generalized permutahedron associated to \(W\). The generalized permutahedron of \(W\) is given as the polytope realizing the cellular complex dual to the simplicial complex cut out by the reflection hyperplanes of \(W\) on the unit sphere \(S^{n-1}\) (here we assume that \(W\) is of rank \(n\) and realized in the canonical way as a group generated by reflections in real \(n\)-space). The second main result shows that the boundary components of \(M\) of a fixed type form a Coxeter matroid as well. This then allows to define a map \(\partial\) on the graded (by the rank of the Coxeter matroid) free \(\mathbb{Z}/2\mathbb{Z}\)-module generated by all Coxeter matroids of a Coxeter group \(W\). The third theorem of the paper then verifies the assertion that \(\partial\) is indeed a differential.