  We show that chaotic classical dynamics associated to the volume of discrete
grains of space leads to quantal spectra that are gapped between zero and
nonzero volume. This strengthens the connection between spectral discreteness
in the quantum geometry of gravity and tame ultraviolet behavior. We complete a
detailed analysis of the geometry of a pentahedron, providing new insights into
the volume operator and evidence of classical chaos in the dynamics it
generates. These results reveal an unexplored realm of application for chaos in
quantum gravity.
