  The optimal N qubit states featuring highest sensitivity to small
misalignment of cartesian reference frames are found using the Quantum
Cramer-Rao bound. It is shown that the optimal states are supported on the
symmetric subspace and hence are mathematically equivalent to a single spin
J=N/2. Majorana representation of spin states is used to reveal a beautiful
connection between the states optimal for aligning reference frames and the
platonic solids.
