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This paper introduces a cube-based reconfigurable robot that utilizes an electromagnet-based actuation framework to reconfigure in three dimensions via pivoting. While a variety of actuation mechanisms for self-reconfigurable robots have been explored, they often suffer from cost, complexity, assembly and sizing requirements that prevent scaled production of such robots. To address this challenge, we use an actuation mechanism based on electromagnets embedded into the edges of each cube to interchangeably create identically or oppositely polarized electromagnet pairs, resulting in repulsive or attractive forces, respectively. By leveraging attraction for hinge formation, and repulsion to drive pivoting maneuvers, we can reconfigure the robot by voxelizing it and actuating its constituent modules - termed Electrovoxels - via electromagnetically actuated pivoting. To demonstrate this, we develop fully untethered, three-dimensional self-reconfigurable robots and demonstrate 2D and 3D self-reconfiguration using pivot and traversal maneuvers on an air-table and in microgravity on a parabolic flight. This paper describes the hardware design of our robots, its pivoting framework, our reconfiguration planning software, and an evaluation of the dynamical and electrical characteristics of our system to inform the design of scalable self-reconfigurable robots.