A reasonably general model of a liquid crystal is achieved by a continuum consisting of microscopic rigid bodies. Within this model it is possible to deal with chiral molecules as well as simple rod-like particles forming a conventional nematic liquid crystal. The configuration space of a rigid body is the rotation group SO(3); the configuration space of a "nematic" is - with regard to the head-tail symmetry the projective plane P(2). By replacing both manifolds by their universal coverings (S-3 and S-2, resp.) the internal symmetry of the fluid can be represented by a generalized (non-normalized) director. Within this mathematical framework mesoscopic balance equations are formulated which are applicable in the biaxial case of chiral molecules and in the uniaxial case of rod-like particles. Finally it is shown how constitutive equations can be derived by calculating averages of mesoscopic quantities with respect to an orientation distribution function which characterizes the orientational order of the liquid crystal.