  In hyperbolic space, the angle of intersection and distance classify pairs of
totally geodesic hyperplanes. A similar algebraic invariant classifies pairs of
hyperplanes in the Einstein universe. In dimension 3, symplectic splittings of
a 4-dimensional real symplectic vector space model Einstein hyperplanes and the
invariant is a determinant. The classification contributes to a complete
disjointness criterion for crooked surfaces in the 3-dimensional Einstein
universe.
