The study of crystalline approximant structures is an important way to understand the local order in quasicrystalline phases. We compare here high-resolution electron microscopy (HREM) image simulations of the cubic approximant phase R-Al5CuLi3with experimental HREM images of the icosahedral Al5CuLi3phase. Local two-dimensional (2D) arrangements such as Penrose tiles of different scales and projections of icosahedral clusters (triacontahedra) are found to be common to both phases, confirming the close similarity of their short and medium-range order. The shape and decoration of three-dimensional (3D) tiles is suggested from their 2D projection. A 2D and 3D inflation rule, comparable with that expected in the icosahedral phase is demonstrated in the approximant phase.