  Velocity dispersion $\sigma$, radius $R$ and luminosity $L$ of elliptical
galaxies are known to be related, leaving only two degrees of freedom and
defining the so-called ``fundamental plane". In this {\em Letter} we present
observational evidence that rich galaxy clusters exhibit a similar behaviour.
Assuming a relation $L \propto R^{\alpha}\sigma^{2 \beta}$, the best-fit values
of $\alpha$ and $\beta$ are very close to those defined by galaxies. The
dispersion of this relation is lower than 10 percent, i.e. significantly
smaller than the dispersion observed in the $L-\sigma$ and $L-R$ relations. We
briefly suggest some possible implications on the spread of formation times of
objects and on peculiar velocities of galaxy clusters.
