This surface is formed by the end of the phase velocity vector. That is, the surface is a surface phase velocities of elastic waves in crystals.
sphereplot (wave, phi = 0 .. 2 * Pi, theta = 0 .. Pi, axes = BOXED, labels = [m / s, m / s, m / s]);
Here the "wave" depends on the direction cosine phi and theta, as well as from the other constant values.