  A theorem of Delzant states that any symplectic manifold $(M,\om)$ of
dimension $2n$, equipped with an effective Hamiltonian action of the standard
$n$-torus $\T^n = \R^{n}/2\pi\Z^n$, is a smooth projective toric variety
completely determined (as a Hamiltonian $\T^n$-space) by the image of the
moment map $\phi:M\to\R^n$, a convex polytope $P=\phi(M)\subset\R^n$. In this
paper we show, using symplectic (action-angle) coordinates on $P\times \T^n$,
how all $\om$-compatible toric complex structures on $M$ can be effectively
parametrized by smooth functions on $P$. We also discuss some topics suited for
application of this symplectic coordinates approach to K\"ahler toric geometry,
namely: explicit construction of extremal K\"ahler metrics, spectral properties
of toric manifolds and combinatorics of polytopes.
