  Geometrical frustration in spin systems often results in a large number of
degenerate ground states. In this work we study the antiferromagnetic Ising
model on the three dimensional swedenborgite lattice which is a specific
stacking of Kagom\'e and triangular layers. The model contains two exchange
couplings, one within the Kagom\'e layer, another one in between Kagom\'e and
triangular layers. We determine the phase diagram with and without easy axis
magnetic field and calculate the ground state degeneracy explicitly in terms of
the residual entropy. At zero field we find two different ground state
manifolds separated by a first order transition at T = 0 and equal exchange
couplings. We also determine the T = 0 phase diagram in a magnetic field and
find a rich phase diagram with both degenerate and non-degenerate phases
depending on the field strength and out-of-plane coupling.
