We investigate the basic laws that determine the global structure and metal abundance of elliptical galaxies. The existence of the Fundamental Plane has been considered to imply that the virial theorem is the only structural constraint for giant ellipticals. However, we show that giant ellipticals do not uniformly cover the Fundamental Plane, but are located in a band which is not the result of selection effects. This 'Fundamental Band' implies a second constraint between scalelength and galaxy mass. On the basis of this result, we present a new framework in which the structure and metal abundance of giant ellipticals are determined by only three fundamental relations: M is-proportional-to R[upsilon2], M is-proportional-to R(zeta) and Z is-proportional-to [upsilon2]xi, where M is the galaxy mass, R is the half-mass radius, [upsilon2] is the mean square speed of the system's stars and Z is the average metallicity of the stellar population; zeta and xi are constants. Xi is uniquely determined from the observations. The value of zeta, however, depends on the assumed scaling laws that relate M and R to the observed luminosity and half-light radius. We assume M/L is-proportional-to M(eta) and R/R(e) is-proportional-to M(lambda). The two constants eta and lambda are mutually constrained by observations, but their values are not uniquely determined. All the wide variety of observed global correlations can be derived as simple combinations of these fundamental relations. This simple framework provides new insights into the intrinsic differences between giant and dwarf ellipticals. The observed universality of the luminosity- and metallicity-velocity dispersion correlations strongly suggests a simple solution within our framework in which zeta, xi and eta adopt the same values for both dwarf and giant ellipticals. In this case, we show that the dependence of R/R(e) on galaxy mass is the only difference between the two galaxy families. We compare this framework with a theoretical scenario of galaxy formation that combines the hierarchical clustering and the galactic wind models. This picture provides a consistent explanation of the fundamental relations of all elliptical galaxies, assuming R/R(e) approximately constant for dwarf ellipticals while, for giant ellipticals, we find that R/R(e) must be a decreasing function of galaxy mass.
