The isosurface plot in two perpendicular planes with the contour slice plot (in the vertical plane) for the 3D electron-density map. (a) The isometric view with the position `a' indicated by an arrow and dotted circle and recognized as the split atomic site on the dodecahedron (section through the dodecahedron marked with dark blue line). The splitting occurs perpendicularly to the cluster's radial direction which is a twofold direction and corresponds to the position indicated by the white arrow in Fig. 2(b). The outline of the RTH cluster is drawn with the red line. Additionally, the outline of the outer icosahedron is marked with an orange line; (b) the top view of (a). (c) The isometric view with the position `b' recognized as the split atomic site on the outer icosahedron along a threefold direction. Such a split position corresponds to that indicated by the white arrow in Fig. 2(c). The contour of the RTH cluster is drawn with the red line alongside the contour of the #2 icosahedron that is marked with an orange line and the contour of the #3 dodecahedral shell marked with a dark blue line; (d) the top view of (c). The specific directions are indicated with red arrows. The positions of the planes in which the electron densities are calculated in the isometric views in (a) and (c) are pictured with grey planes together with the orientation of the vectors in the icosahedral setting.