  We construct a 2-parameter family of unitarily equivalent irreducible
representations of the triply extended group $\g$ of translations of
$\mathbb{R}^{4}$ associated with a family of its 4-dimensional coadjoint orbits
and show how a continuous 2-parameter family of gauge potentials emerges from
these unitarly equivalent representations. We show that the Landau and the
symmetric gauges of noncommutative quantum mechanics, widely used in the
literature, in fact, belong to this 2-parameter family of gauges. We also
provide an explicit construction of noncommutative 4-tori and compute the
associated star products using the unitary dual of the group $\g$ that was
studied at length in an earlier paper (\cite{ncqmjpa}). Finally, we construct
projective modules over such noncommutative 4-tori and compute constant
curvature connections on them using Rieffel's method.
