Bilinski (1960) noted that by collapsing any one of the five zones of the rhombic icosahedron, a second rhombic dodecahedron
distinct from the dual polyhedron of the cuboctahedron
can be made whose faces are golden rhombi (Chilton
and Coxeter 1963). While this solid first appeared much earlier in a book by John
Lodge Cowley (1752), where it was labeled as the "dodecarhombus," it is
now commonly known as the Bilinski dodecahedron.
A net of the Bilinski dodecahedron is illustrated above.
Bilinski, S. "Über die Rhombenisoeder." Glasnik15, 251-263, 1960.Chilton, B. L. and Coxeter, H. S. M. "Polar
Zonohedra." Amer. Math. Monthly70, 946-951, 1963.Cowley,
J. L. Plate 5, Fig. 16 in Geometry Made Easy; Or, a New and Methodical
Explanation of the Elements of Geometry. London: 1752.Coxeter, H. S. M.
"The Classification of Zonohedra by Means of Projective Diagrams." J.
de Math. pures et appl.41, 137-156, 1962.Coxeter, H. S. M.
Ch. 4 in The
Beauty of Geometry: Twelve Essays. New York: Dover, 1999.Cromwell,
P. R. Polyhedra.
New York: Cambridge University Press, p. 156, 1997.Grünbaum,
B. "The Bilinski Dodecahedron and Assorted Parallelohedra, Zonohedra, Monohedra,
Isozonohedra, and Otherhedra." Math. Intel.32, 5-15, 2010.Hart,
G. W. "A Color-Matching Dissection of the Rhombic Enneacontahedron."
Symmetry: Culture and Science11, 183-199, 2000.
