Lithium-ion battery cathode materials have relied on cationic redox reactions until the recent discovery of anionic redox activity in Li-rich layered compounds which enables capacities as high as 300 mAh g(-1). In the quest for new high-capacity electrodes with anionic redox, a still unanswered question was remaining regarding the importance of the structural dimensionality. The present manuscript provides an answer. We herein report on a beta-Li2IrO3 phase which, in spite of having the Ir arranged in a tridimensional (3D) framework instead of the typical two-dimensional (2D) layers seen in other Li-rich oxides, can reversibly exchange 2.5 e(-) per Ir, the highest value ever reported for any insertion reaction involving d-metals. We show that such a large activity results from joint reversible cationic (Mn+) and anionic (O-2)(n-) redox processes, the latter being visualized via complementary transmission electron microscopy and neutron diffraction experiments, and confirmed by density functional theory calculations. Moreover, beta-Li2IrO3 presents a good cycling behaviour while showing neither cationic migration nor shearing of atomic layers as seen in 2D-layered Li-rich materials. Remarkably, the anionic redox process occurs jointly with the oxidation of Ir4+ at potentials as low as 3.4 V versus Li+/Li-0, as equivalently observed in the layered alpha-Li2IrO3 polymorph. Theoretical calculations elucidate the electrochemical similarities and differences of the 3D versus 2D polymorphs in terms of structural, electronic and mechanical descriptors. Our findings free the structural dimensionality constraint and broaden the possibilities in designing high-energy-density electrodes for the next generation of Li-ion batteries.