  Quasi-equilibrium models of uniformly rotating axisymmetric and triaxial
quark stars are computed in general relativistic gravity scenario. The
Isenberg-Wilson-Mathews (IWM) formulation is employed and the Compact Object
CALculator (COCAL) code is extended to treat rotating stars with finite surface
density and new equations of state (EOSs). Besides the MIT bag model for quark
matter which is composed of de-confined quarks, we examine a new EOS proposed
by Lai and Xu that is based on quark clustering and results in a stiff EOS that
can support masses up to $3.3M_\odot$ in the case we considered. We perform
convergence tests for our new code to evaluate the effect of finite surface
density in the accuracy of our solutions and construct sequences of solutions
for both small and high compactness. The onset of secular instability due to
viscous dissipation is identified and possible implications are discussed. An
estimate of the gravitational wave amplitude and luminosity based on quadrupole
formulas is presented and comparison with neutron stars is discussed.
