  We study quasiequilibrium solutions of triaxially deformed rotating compact
stars -- a generalization of Jacobi ellipsoids under relativistic gravity and
compressible equations of state (EOS). For relatively stiff (piecewise)
polytropic EOSs, we find supramassive triaxial solutions whose masses exceed
the maximum mass of the spherical solution, but are always lower than those of
axisymmetric equilibriums. The difference in the maximum masses of triaxial and
axisymmetric solutions depends sensitively on the EOS. If the difference turns
out to be only about 10%, it will be strong evidence that the EOS of high
density matter becomes substantially softer in the core of neutron stars. This
finding opens a novel way to probe phase transitions of high density nuclear
matter using detections of gravitational waves from new born neutron stars or
magnetars under fallback accretion.
