The Great Rhombic Enneacontahedron

The above figure is the great rhombic enneacontahedron (VRML, OFF).  In common with the rhombic enneacontahedron, it consists of sixty fat rhombi ('R') (gold coloured) as found in the rhombic dodecahedron and thirty thin rhombi ('r') (bronze coloured) as found in the medial rhombic triacontahedron.  It is isomorphous to the rhombic enneacontahedron.  The thin rhombi are all hidden within the figure.  The right image above shows the figure with the fat rhombi as frames and the thin rhombi solid.

A comparison of the vertices between the two polyhedra shows the following relationships:

rhombic enneacontahedron great rhombic enneacontahedron
3-fold 2Ro.ra
5-fold 5Ra 5Ra / 2
6-fold 3(Ra.ra) 3( / 2

Notation:  R: fat rhombus,  r: thin rhombus, a: acute angle of rhombus, o: obtuse angle.

The rhombic enneacontahedron can be faceted to form a dodecahedron by taking the long diagonal of the thin rhombi (above left).  The short diagonals of the thin rhombi in the great rhombic enneacontahedron form  a great stellated dodecahedron (above right).