Antenna arrays are essential elements in modern wireless communication technologies. Capabilities to perform real-time beamforming with millisecond-scale latencies enable supporting frontier 5G communication protocols. Being based on standard lithography methods, printed board antenna arrays are two-dimensional by design. However, exploration of the third dimension allows for obtaining new capabilities, including wide-angle scanning, broadband impedance matching, higher directivity, and several others. Here we demonstrate an additively manufactured volumetric antenna array, where each individual element is 3D-printed and subsequently metalized with the aid of electrochemical deposition. Additive manufacturing is foreseen to provide capabilities of a complete production cycle, including electronics and peripheries, being fabricated within the same machine. Here, the full potential of volumetric antenna arrays will be revealed.