  It is still a matter of debate to understand the equation of state of cold
supra-nuclear matter in compact stars because of unknown on-perturbative strong
interaction between quarks. Nevertheless, it is speculated from an
astrophysical view point that quark clusters could form in cold quark matter
due to strong coupling at realistic baryon densities. Although it is hard to
calculate this conjectured matter from first principles, one can expect the
inter-cluster interaction to share some general features to nucleon-nucleon
interaction. We adopt a two-Gaussian component soft-core potential with these
general features and show that quark clusters can form stable simple cubic
crystal structure if we assume Gaussian form wave function. With this
parameterizing, Tolman-Oppenheimer-Volkoff equation is solved with reasonable
constrained parameter space to give mass-radius relation of crystalline solid
quark star. With baryon densities truncated at 2 times nuclear density at
surface and range of interaction fixed at 2fm we can reproduce similar
mass-radius relation to that obtained with bag model equations of state. The
maximum mass ranges from about 0.5 to 3 solar mass. Observed maximum pulsar
mass (about 2 solar mass) is then used to constrain parameters of this simple
interaction potential.
