  We show that two-dimensional phononic crystals exhibit Dirac cone dispersion
at k=0 by exploiting dipole and quadrupole accidental degeneracy. While the
equi-frequency surface of Dirac cone modes is isotropic, such systems exhibit
"super-anisotropy", meaning that only transverse waves are allowed along
certain directions while only longitudinal waves are allowed along some other
directions. Only one mode, not two, is allowed near the Dirac point, and only
two effective parameters, not four, are needed to describe the dispersion.
Effective medium theory finds that the phononic crystals have effectively zero
mass density and zero 1/C44 at the Dirac point. Numerical simulations are used
to demonstrate the unusual elastic wave properties near the Dirac point
frequency.
