  We present a geometry-based discussion of possible vortex configurations in
the mixed state of anisotropic type-II superconductors. It is shown that, if
energy considerations assign six nearest neighbors to each vortex, two distinct
modifications of the vortex lattice are possible. It is expected that certain
conditions lead to a first order phase transition from one modification of the
vortex lattice to the other upon varying the external magnetic field.
