We analyze single-stellar-population (SSP) equivalent parameters for 50 local elliptical galaxies as a function of their structural parameters. These galaxies fill a two-dimensional plane in the four-dimensional space of [Z/H], log t, log $sigma$, and [E/Fe]. SSP age and velocity dispersion can be taken as the two independent parameters that specify a galaxys location in this ``hyperplane. The hyperplane can be decomposed into two sub-relations: (1) a ``Z-plane, in which [Z/H] is a linear function of log $sigma$ and log t; and (2) a relation between [E/Fe] and $sigma$ in which [E/Fe] is larger in high-$sigma$ galaxies. Cluster and field ellipticals follow the same hyperplane, but their ($sigma$,t) distributions within it differ. Nearly all cluster galaxies are old; the field ellipticals span a large range in SSP age. The tight Mg--$sigma$ relations of these ellipticals can be understood as two-dimensional projections of the metallicity hyperplane showing it edge-on; the tightness of these relations does not necessarily imply a narrow range of ages at fixed $sigma$. The relation between [E/Fe] and $sigma$ is consistent with a higher effective yield of Type II SNe elements at higher $sigma$. The Z-plane is harder to explain and may be a powerful clue to star formation in elliptical galaxies if it proves to be general. Present data favor a ``frosting model in which low apparent SSP ages are produced by adding a small frosting of younger stars to an older base population. If the frosting abundances are close to or slightly greater than the base population, simple two-component models run along lines of constant $sigma$ in the Z-plane, as required. This favors star formation from well-mixed pre-enriched gas rather than unmixed low-metallicity gas from an accreted object. (Abridged)
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