Modern physics has characterized spacetime, the interactions between particles, but not the nature of the particles themselves. Previous models of the electron have not specified its substance nor justified its cohesion. Here we present a relativistic electrodynamical model of the electron at rest, founded on natural interpretations of observables. Essentially intertwined positively and negatively charged subparticles revolve at light velocity in coplanar circular orbits, forming some coherent "envelope"and "nucleus", possibly responsible for its wavelike and corpuscular behaviors, respectively. We show that the model can provide interpretations of fundamental constants, satisfy the Virial theorem, and exhibit cohesion and stability without invoking Poincare stresses. Remarkably, the stability condition allows predicting electron mass, regarded as being a manifestation of its total (kinetic and potential) electromagnetic cohesion energy, and muon mass, directly from the substructure. Our study illustrates the possibility of constructing causal and objectively realist models of particles beneath the Compton scale. Finally, wave-corpuscle duality and the relation to quantum mechanics are discussed in the light of our electron model.