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A type of closed exterior algebra in R 3 under the cross product is revealed to hold between differential forms from the three Whittaker scalar potentials, associated with the fields of a moving electron. A special algebraic structure is revealed in the context of Clebsch reparametrization of these scalars, and a special prescription for the construction of permutation invariant electromagnetic fields is given as well as a superposition with parallel electric and magnetic components.doi:10.2528/pierl13071904 fatcat:32ilqi4dsbggtcurmgfu3mvmrm