  We study genuine tripartite entanglement shared among the spins of three
localized fermions in the non-interacting Fermi gas at zero temperature.
Firstly, we prove analytically with the aid of entanglement witnesses that in a
particular configuration the three fermions are genuinely tripartite entangled.
Then various three-fermion configurations are investigated in order to quantify
and calculate numerically the amount of genuine tripartite entanglement present
in the system. Further we give a lower and an upper limit to the maximum
diameter of the three-fermion configuration below which genuine tripartite
entanglement exists and find that this distance is comparable with the maximum
separation between two entangled fermions. The upper and lower limit turn to be
very close to each other indicating that the applied witness operator is well
suited to reveal genuine tripartite entanglement in the collection of
non-interacting fermions.
