  We show that the n-dimensional MICZ-Kepler system arises from symplectic
reduction of a simple mechanical system on the cone over the rotation group
SO(n). As a corollary we derive an elementary formula for its general solution.
The punch-line of our computation is that the additional MICZ-Kepler
$|\phi|^2/r^2$ type potential term is the rotational part of the cone's kinetic
energy.
