By certain variations of the phase of quasiperiodic tilings, vertices can be permuted and even transported to infinity in a diffusive way. In a preceding article, we have studied such a motion for the icosahedral Ammann - Kramer - Penrose tiling. The `quantum of diffusion' occurs in a triacontahedral cage, where atoms in sets of three and seven can be interchanged arbitrarily. Here we show that these kinetic processes can be represented by the `stellated polyhedra' and , respectively.