Double Rhombic Icosahedron
This Demonstration shows the structure of the double rhombic icosahedron. It consists of 10 prolate rhombohedra (on the inside), 10 rhombic dodecahedra of the second kind, 2 rhombic icosahedra, and 10 oblate rhombohedra (on the outside).
The structure of rhombic icosahedron and double rhombic icosahedron was observed by Japanese mathematician Koji Miyazaki in 1977.
 W.W. R. Ball and H.M.S. Coxeter, Mathematical Recreations and Essays, 13th ed., New York: Dover, 1987 p. 161.