  3D nano-architectures present a new paradigm in modern condensed matter
physics with numerous applications in photonics, biomedicine, and spintronics.
They are promising for the realisation of 3D magnetic nano-networks for
ultra-fast and low-energy data storage. Frustration in these systems can lead
to magnetic charges or magnetic monopoles, which can function as mobile, binary
information carriers. However, Dirac strings in 2D artificial spin ices bind
magnetic charges, while 3D dipolar counterparts require cryogenic temperatures
for their stability. Here, we present a micromagnetic study of a
highly-frustrated 3D artificial spin ice harboring tension-free Dirac strings
with unbound magnetic charges at room temperature. We use micromagnetic
simulations to demonstrate that the mobility threshold for magnetic charges is
by $\SI{2}{eV}$ lower than their unbinding energy. By applying global magnetic
fields, we steer magnetic charges in a given direction omitting unintended
switchings. The introduced system paves a way towards 3D magnetic networks for
data transport and storage
