  We study the ordered equilibrium structures of patchy particles where the
patches are located on the surface of the colloid such that they form a regular
tetrahedron. Using optimization techniques based on ideas of evolutionary
algorithms we identify possible candidate structures. We retain not only the
energetically most favourable lattices but also include a few energetically
less favourable particle arrangements (i.e., local minima on the enthalpy
landscape). Using suitably developed Monte Carlo based simulations techniques
in an NPT ensemble we evaluate the thermodynamic properties of these candidate
structures along selected isobars and isotherms and identify thereby the
respective ranges of stability. We demonstrate on a quantitative level that the
equilibrium structures at a given state point result from a delicate compromise
between entropy, energy (i.e., the lattice sum) and packing.
