The combination of optical and X-ray data provides a key to the fundam
ental properties of clusters of galaxies. For our analysis, we choose
a complete sample of nearby clusters in the redshift range from 0.02 t
o 0.05. Using the COSMOS-and ROSAT-data we derive robust optical and X
-ray parameters from surface brightness profiles. In particular, we us
e the optical and Xray luminosity and the half-light radii in both ene
rgy bands for the analysis. We derive several monovariant relations fo
r different morphological classes of galaxy clusters. Under the assump
tion that the cluster is virialized and in hydrostatic equilibrium we
estimate the mass to light ratio and the dark matter fraction. The rem
arkably low scatter in this relation reveals the existence of a fundam
ental plane of clusters of galaxies in the optical and X-ray parameter
space. In addition, the comparison with structures on smaller scales
supports the hierarchical clustering scenario.