Rhombic Dodecahedron

The Dual Polyhedron of the Cuboctahedron, also sometimes called the Rhomboidal Dodecahedron (Cotton1990). Its 14 vertices are joined by 12 Rhombuses, and one possible way to construct it is known as theBauspiel. The rhombic dodecahedron is a Zonohedron and a Space-Filling Polyhedron. The vertices aregiven by (, , ), (, 0, 0), (0, , 0), (0, 0, ).

The edges of the Cube-Octahedron Compound intersecting in the points plotted above are the diagonals ofRhombuses, and the 12 Rhombuses form a rhombic dodecahedron (Ball and Coxeter 1987).

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, p. 137, 1987.

Cotton, F. A. Chemical Applications of Group Theory, 3rd ed. New York: Wiley, p. 62, 1990.

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