Cayley Cubic is an algebracic surface of degree 3. Its formula is:

4 * (x^2 + y^2 + z^2) + 16*x*y*z - 1 == 0

Cayley Cubic has the same symmetry as tetrahedron. Its center is shaped like a tetrahedron. It has asymptotic faces.

Mathematica file

cayley_cubic.gcf