  When magnetic moments (spins) are regularly arranged in a geometry of a
triangular motif, the spins may not satisfy simultaneously their interactions
with their neighbors. This phenomenon, called frustration, leads to numerous
energetically equivalent magnetic states (ground states), which results in
exotic states such as spin liquid and spin ice. Here we report an alternative
situation: a system that, classically, is to be a liquid in the clean limit
freezes into a glassy state induced by quantum fluctuations. The case in point
is a frustrated magnet in which spins are arranged in a triangular network of
bi-pyramids. When taking into account quantum corrections, the classical
degeneracy is broken into a set of local minima in a rugged energy landscape,
which are separated by large energy barriers, over a finite number of
degenerate, periodic, ground states. The appearance of large barriers is due to
the absence of local zero-energy modes that are typical in spin-liquid
candidate systems. We establish this by mapping the set of local energy minima
states into a tiling with colored hexagonal tiles. We show that the system
exhibits a large number of aperiodic tessellations. The configuration entropy
of the local minima is extremely sensitive to boundary conditions, scaling with
the boundary length rather than its volume. The low temperature thermodynamics
is also discussed to compare it with other glassy materials.
