Abstract. Flow diagrams for the differential equations of classical electromagnetism have previously been published as expository tools by Tonti and Deshamps. Electromagnetic duality, resulting from the theoretical magnetic monopole, and constitutive duality, such as between the E and D fields, are fundamental concepts of the theory. However, in neither the Tonti nor the Deshamps diagram do both dualities correspond to reflection in a line or plane. Hyperplane reflection, among all the nonidentical isometries (distance-preserving symmetry operations) of the Euclidean plane or space, is the only one that is both the most elementary from which the others can be composed, and also very simple, or even simplest, to visualize. We present a new flow diagram for the differential equations of the space-time split, (3+1)-dimensional, theory of classical electromagnetism in arbitrary media at rest. It is drawn as a lattice of rectangular parallelepipeds to allow two reflection planes. The horizontal reflection plane mirrors the field quantities with their electromagnetic duals; the vertical reflection plane mirrors the field quantities with their constitutive duals. As key to the elegant symbolic expression of these symmetries, we follow Burke by using both ordinary and twisted differential forms, possessing both inner and outer orientations, to write the equations in manifestly parity-invariant form. The previously unnamed ``Lorentz functions" and ``surge subsources" are represented. We exhibit Nisbet's direct plus dual gauge theory of the Hertz and stream potentials in this fitting arena. The origin of the diagram is briefly discussed.
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