At room temperature, triangular Co islands can be grown on Cu(111), protruding two atomic layers high above the Cu surface. Two different orientations of the triangles are observed, indicating a stacking fault with respect to the fcc stacking of the Cu substrate in one case. We have studied the structural, electronic, and magnetic properties of these islands with spin-averaged and spin-resolved scanning tunneling spectroscopy at low temperatures. Using a non-magnetic tunneling tip, we found the electronic properties of the differently oriented islands to be clearly inequivalent. In differential conductance (dI/dV) maps this leads to strong contrasts at the appropriate energies with signal asymmetries as high as 50 percent. Applying a magnetic tip, another source of contrast with similar strength becomes accessible, originating from the perpendicular magnetization of the islands.@footnote 1@ We discuss the Co spin polarization which is strongly energy dependent and repeatedly changes sign. Quite similar to the Cu substrate surface, the Co islands exhibit a standing wave pattern in the local density of states. In the case of Co, however, the responsible dispersive state is spin-polarized. This spin imbalance modifies the oscillation amplitude. A comparison of the Cu and Co patterns as a function of energy reveals yet another difference: while the Cu patterns indicate two-dimensional free-electron gas behavior, the Co patterns are affected by lateral electron confinement. We compare our observations with models based on an exact solution of the particle-in-a-triangular-box problem@footnote 2@ and a multiple scattering approach.@footnote 3@ @FootnoteText@ @footnote 1@ O. Pietzsch, A. Kubetzka, M. Bode, and R. Wiesendanger, Phys. Rev. Lett. 92, 057202 (2004).@footnote 2@ H.R. Krishnamurthy, H.S. Mani, and H.C. Verma, J. Phys. A: Math. Gen. 15, 2131 (1982).@footnote 3@ E.J. Heller, M.F. Crommie, C.P. Lutz, and D.M. Eigler, Nature 369, 464 (1994).