We show that the near surface structure of lamellae ABC triblock copolymer mesostructures can deviate considerably from the "ideal" surface anticipated from the bulk structure of the material. Varying the molecular architecture and the surface energy difference between the respective blocks, we show that such surface reconstructions are caused by a complex balance of enthalpic and entropic contributions to the free energy of the system. The results are compared to the well-known surface behavior of classical crystals and experimental conditions for what may be called "block copolymer surface science" are discussed.