The structure of the alpha-(Al,Si)CuFe approximant phase is determined by a single-crystal X-ray diffraction study and compared to the ideal structure obtained by the perpendicular shear method of the parent icosahedral phase. It is shown that the local environments (typical atomic clusters) of the two phases are similar and expand significantly farther than the size of the unit cell of the approximant. The orbit Al(2) issuing from the theoretical icosahedral model corresponding to the inner dodecahedron of the Mackay-type cluster is not found in the approximant and is replaced by a partially occupied inner icosahedron with an unusually large Debye-Waller factor.