Stella Octangula
A Polyhedron Compound composed of a Tetrahedron and its Reciprocal (a second Tetrahedron rotated180° with respect to the first). The stella octangula is also called a Stellated Tetrahedron. It can beconstructed using the following Net by cutting along the solid lines, folding back along the plainlines, and folding forward along the dotted lines.
Another construction builds a single Tetrahedron, then attaches four tetrahedral caps, one to each face.
The edges of the two tetrahedra form the 12 Diagonals of a Cube. The solid common toboth 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.