  The classical Ising model on the frustrated 3d swedenborgite lattice has
disordered spin liquid ground states for all ratios of inter- and intra-planar
couplings. Quantum fluctuations due to a transverse field give rise to several
exotic quantum phenomena. In the limit of weakly coupled Kagom\'e layers we
find a 3d version of disorder by disorder. For large out-of-plane couplings 1d
macro-spins are formed which realize a disordered macro-spin liquid on an
emerging triangular lattice. Signatures of this dimensional reduction are also
found in critical exponents of the quantum phase transition out of the fully
polarized phase into the macro-spin liquid displaying quantum criticality
typical for 2d quantum systems.
