Cube-Octahedron Compound

A Polyhedron Compound composed of a Cube and its Dual Polyhedron, the Octahedron. The 14 vertices are given by ($\pm 1$, $\pm 1$, $\pm 1$), ($\pm 2$, 0, 0), (0, $\pm 2$, 0), (0, 0, $\pm 2$).

The solid common to both the Cube and Octahedron (left figure) in a cube-octahedron compound is a Cuboctahedron (middle figure). The edges intersecting in the points plotted above are the diagonals of Rhombuses, and the 12 Rhombuses form a Rhombic Dodecahedron (right figure; Ball and Coxeter 1987).

See also Cube, Cuboctahedron, Octahedron, Polyhedron Compound

References

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

Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, p. 158, 1969.

Cundy, H. and Rollett, A. Mathematical Models, 3rd ed. Stradbroke, England: Tarquin Pub., p. 130, 1989.