Twelve around one
The animation above shows how the Rhombic Triacontahedron fits perfectly into one of the twelve depressions of the Stellation of the Rhombic Triacontahedron.
The animation above shows how twelve Rhombic Triacontahedra can fit or nest into the twelve depressions of the Stellation of the Rhombic Triacontahedron. On each Triacontahedron, there are five rhombic faces that mate up with adjacent Rhombic Triacontahedron rhombi.
The animation above shows twelve one fourths of a Rhombic Triacontahedron filling in the twelve depressions, creating a larger Rhombic Triacontahedron. The larger Rhombic Triacontahedron shares the long diagonal of the initial one fourth Rhombic Triacontahedron’s rhombic face, except that it is the short diagonal of the larger Rhombic Triacontahedron. The larger Rhombic Triacontahedron is increased by a linear factor of phi/tau or 1.618034. The resulting volumetric increase is phi/tau to the third power or 4.236068.
The animation above shows how four T-modules that form a rhombic face, can be folded open so the radial lengths of the T-modules form the next larger or next size up rhombic face. This larger rhombic face has the diagonals increased by the Golden Proportion on both diagonals of the smaller rhombic face.
