[en] A canonical realization of the so(4,2) algebra for three degrees of freedom is determined, which conserves the essential properties of the so(4,2) algebra associated by Gyorgyi to the Kepler problem, Bacry-Gyorgyi coordinates are generalized. The canonical realization of the so(4,2) algebra is related to a classical central motion where it plays a role similar to the role played by the so(4,2) algebra in the Kepler problem. (author)