  Elliott's SU(3) model is at the basis of the shell-model description of
rotational motion in atomic nuclei. We demonstrate that SU(3) symmetry can be
realized in a truncated shell-model space if constructed in terms of a
sufficient number of collective $S$, $D$, $G$, $\dots$ pairs (i.e., with
angular momentum zero, two, four, $\dots$) and if the structure of the pairs is
optimally determined either by a conjugate-gradient minimization method or from
a Hartree-Fock intrinsic state. We illustrate the procedure for 6 protons and 6
neutrons in the $pf$ ($sdg$) shell and exactly reproduce the level energies and
electric quadrupole properties of the ground-state rotational band with $SDG$
($SDGI$) pairs. The $SD$-pair approximation without significant
renormalization, on the other hand, cannot describe the full SU(3)
collectivity. A mapping from Elliott's fermionic SU(3) model to systems with
$s$, $d$, $g$, $\dots$ bosons provides insight into the existence of a
decoupled collective subspace in terms of $S$, $D$, $G$, $\dots$ pairs.
