  We derive several versions of the cell theory for a crystal phase of hard
equilateral triangles. To that purpose we analytically calculated the free area
of a frozen oriented or freely rotating particle inside the cavity formed by
its neighbours in a chiral configuration of their orientations. From the most
successful versions of the theory we predict an equation of state which,
despite being derived from a crystal configuration of particles, describes very
reasonably the equation of state of the 6-atic liquid-crystal phase at packing
fractions not very close from the isotropic-6-atic bifurcation. Also, the same
equation of state performs well when compared to that from MC simulations for
the stable crystal phase. The agreement can even be improved by selecting
adequate values for the angle of chirality.Despite the success of two of the
versions of the theory for the pressure, we show that the free-energy is an
increasing function of the angle of chirality, implying that the most stable
phase is the achiral phase. Furthermore, we show that possible clustering
effects, such as the formation of perfect chiral hexagonal clusters, which in
turn crystallize into an hexagonal lattice, cannot explain the presence of the
chirality observed in simulations.
