  The quantum spin liquid (QSL) is a highly entangled magnetic state
characterized by the absence of static magnetism in its ground state. Instead,
the spins fluctuate in a highly correlated way down to the lowest temperatures.
The QSL is very rare and is confined to a few specific cases where the
interactions between the magnetic ions cannot be simultaneously satisfied
(known as frustration). Lattices with magnetic ions in triangular or
tetrahedral arrangements which interact via isotropic antiferromagnetic
interactions can generate such a frustration. Three-dimensional isotropic spin
liquids have mostly been sought in materials where the magnetic ions form
pyrochlore or hyperkagome lattices. Here we present a three-dimensional lattice
called the hyper-hyperkagome that enables spin liquid behaviour and manifests
in the compound PbCuTe$_{2}$O$_{6}$. Using a combination of experiment and
theory we show that this system exhibits signs of being a quantum spin liquid
with no detectable static magnetism together with the presence of diffuse
continua in the magnetic spectrum suggestive of fractional spinon excitations.
