Stella Octangula

A Polyhedron Compound composed of a Tetrahedron and its Reciprocal (a second Tetrahedron rotated 180° with respect to the first). The stella octangula is also called a Stellated Tetrahedron. It can be constructed using the following Net by cutting along the solid lines, folding back along the plain lines, and folding forward along the dotted lines.

$\begin{figure}\begin{center}\BoxedEPSF{Stella_Octangula_Net_1.epsf scaled 800}\end{center}\end{figure}$

Another construction builds a single Tetrahedron, then attaches four tetrahedral caps, one to each face.

$\begin{figure}\begin{center}\BoxedEPSF{Stella_Octangula_Net_2.epsf}\end{center}\end{figure}$

The edges of the two tetrahedra form the 12 Diagonals of a Cube. The solid common to both tetrahedra is an Octahedron (Ball and Coxeter 1987).

See also Cube, Octahedron, Polyhedron Compound, Tetrahedron

References

Ball, W. W. R. and Coxeter, H. S. M. Mathematical Recreations and Essays, 13th ed. New York: Dover, pp. 135-137, 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. 129, 1989.