Phononic band gaps (PBGs) are frequency ranges where mechanical waves cannot propagate in a medium. For PBGs to occur the geometry of the medium plays the key part in this so-called metamaterial. Many times, these materials are made of two phases or composites of different elastic constants. We present a PBG material using only a single cellular metallic phase that can effectively block mechanical waves in the upper audible hearing range. In dispersion relation simulations, we numerically predict the existence of PBGs in millimeter-scale cellular structures. In a frequency domain analysis simulation, we show the theoretical transmission behaviour of waves inside the medium and visualize the occurence of PBGs. Gradient-based optimization was used to get geometries with PBGs in lower frequencies. Finally, Ti-6Al-4V samples produced via the additive process of electron beam melting (EBM) were tested in an experiment and verified both simulations. These structures could possibly be used as omnidirectional sound or vibration insulator.