  Using Euler's formula for a network of polygons for 2D case (or polyhedra for
3D case), we show that the number of dynamic\textit{\}degrees of freedom of the
electric field equals the number of dynamic degrees of freedom of the magnetic
field for electrodynamics formulated on a lattice. Instrumental to this
identity is the use (at least implicitly) of a dual lattice and of a (spatial)
geometric discretization scheme based on discrete differential forms. As a
by-product, this analysis also unveils a physical interpretation for Euler's
formula and a geometric interpretation for the Hodge decomposition.
