Let F_0, ... F_n denote hyperplanes in (Euclidean) n-space, where each F_i satisfies an equation F_i1 x_1 + ... + F_in x_n = -F_i0 , normalised so that (F_i1)^2 + ... + (F_in)^2 = 1 . The square matrix determinant | F_ij | has the property that it vanishes when the hyperplanes have some common point. More interestingly, its sign may be used in conjunction with a fixed frame F_1, ..., F_n --- or equivalently, with their intersection point P_0 --- to define the (chromatic) orientation of a variable plane F_0 in a scene as observed from viewpoint P_0 . With F_i0 and F_0j omitted, the remaining order n minor is (related to?) what Coxeter somewhere calls an "n-dimensional cosine", and thence to Gaussian curvature. But does the entire determinant have any established name; does its value represent some natural geometric property of a simplex? Fred Lunnon