In this work, we provide a geometrical framework for the analysis and design of beamformer codebooks with finite number of beamformer vectors. We present a design criterion for good beamfomer codebooks and show the equivalence of the beamformer design problem to two other known problems. First, the beamformer design problem can be directly posed as a problem of packing 2 dimensional subspaces in a 2t dimensional Grassmannian manifold, t being the number of transmit antennas. And second, under certain conditions, the beamformer design problem is equivalent to the construction of unitary space time constellations.