An object colour's Commission Internationale de l'Eclairage XYZ coordinates can change when it is viewed under different illuminants. The set of XYZ coordinates for all object colours, which is called the object-colour solid, likewise varies under different illuminants. This article shows that, despite these changes, some properties are invariant under illuminant transformations. In particular, as long as the illuminant is nowhere zero in the visible spectrum, optimal colours take the same Schrodinger form, and no two optimal colours are metameric. Furthermore, all object-colour solids have the same shape at the origin: they all fit perfectly into the convex cone (which we will call the spectrum cone) generated by the spectrum locus. The spectrum cone, itself, does not vary when the illuminant changes. The object-colour solid for one illuminant can be transformed into the solid for another illuminant, by an easily visualized sequence of expansions and contractions of irregular rings, called zones. (c) 2012 Wiley Periodicals, Inc.