Cubatic phase for tetrapods

We investigate the phase behavior of tetrapods, hard non-convex bodies formed by 4 rods connected under tetrahedral angles. We predict that, depending on the relative lengths of the rods these particles can form a uniaxial nematic phase, and more surprisingly they can exhibit a cubatic phase, a special case of the biaxial nematic phase. These predictions may be experimentally testable, as experimental realizations of tetrapods have recently become available.