Many important questions about the effective behavior of composite materials can be restated as problems in Calculus of Variations, where the unknown is a vector field. One such question is whether every composite can be mimicked by a laminate made with the same constituent materials. The parallel question in the context of Calculus of Variations is whether every rank-one convex function, (i.e. convex along rank-one lines) is quasiconvex. Both questions had been open for a long time before they were settled, and both have been answered in the negative. However, examples settling these questions are unwieldy and hard to construct. In this talk I will produce an aesthetically beautiful example of a rotationally-invariant rank-one convex, nonquasiconvex function. This example comes from the theory of exact relations - formulas that hold for effective tensors of all composites made with a given set of materials, regardless of microstructure.