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 have been open for a long time, and both have been answered in the negative in general. However, the examples settling these questions are unwieldy and hard to construct. In this talk I will produce an esthetically beautiful example of a rotationally-invariant rank-one convex, non-quasiconvex function. This example is the result of a formula that is satisfied by all laminates but fails to hold for all composite materials. The construction is based on the theory of exact relations, giving an algebraic characterization of all sets of equations satisfied by effective tensors of all laminates. Another algebraic condition, that must be satisfied by the equations to hold for all composites, permits us to construct the counterexample.