It is hitherto thought that liquid water is composed of tetrahedrally coordinated molecules with an asymmetric interaction of the central molecule with neighboring molecules. Kuhne et al., Nat. Commun., 2013, 4, 1450 suggested that this asymmetry, energetic rather than geometric, is the cornerstone to reconcile the homogeneous and inhomogeneous viewpoints of liquid water. In order to investigate the geometric origin of that asymmetry, we have scrutinized Molecular Dynamics (MD) simulations of water through a careful analysis of the five-dimensional probability distribution function of Euler angles in which the relative positions and orientations of water molecules are obtained. We demonstrate that, beyond the ubiquitous tetrahedral structure with well-defined molecular dimers, there is a series of possible molecular orientations that define the structure. These orientations are generated by rotating the neighboring molecule around the O-H axis that is involved in the hydrogen bond scheme. Two of the possible orientations have a higher probability, giving rise to two kinds of dimers: one close to the lowest energy of a water dimer in vacuum with an almost perpendicular alignment of the dipole moment, and another one with a parallel orientation of the dipole moment which is less tightly bound. These two different dimers have an effect on the orientation of further water dipole moments up to a distance of approximate to 6 angstrom. Liquid water can therefore be described as a continuous mixture of two kinds of dimers where the hydrogen bonds have the same geometry but the interaction energies are different due to a different mutual orientation of the dipoles of the participating water molecules.