  This paper serves to elucidate the nature of toric duality dubbed in
hep-th/0003085 in the construction for world volume theories of D-branes
probing arbitrary toric singularities. This duality will be seen to be due to
certain permutation symmetries of multiplicities in the gauged linear sigma
model fields. To this symmetry we shall refer as ``multiplicity symmetry.'' We
present beautiful combinatorial properties of these multiplicities and rederive
all known cases of torically dual theories under this new light. We also
initiate an understanding of why such multiplicity symmetry naturally leads to
monodromy and Seiberg duality. Furthermore we discuss certain ``flavor'' and
``node'' symmetries of the quiver and superpotential and how they are
intimately related to the isometry of the background geometry, as well as how
in certain cases complicated superpotentials can be derived by observations of
the symmetries alone.
