  Ring geometries have fascinated experimental and theoretical physicists over
many years. Open rings connected to leads allow the observation of the
Aharonov-Bohm effect, a paradigm of quantum mechanical phase coherence. The
phase coherence of transport through a quantum dot embedded in one arm of an
open ring has been demonstrated. The energy spectrum of closed rings has only
recently been analysed by optical experiments and is the basis for the
prediction of persistent currents and related experiments. Here we report
magnetotransport experiments on a ring-shaped semiconductor quantum dot in the
Coulomb blockade regime. The measurements allow us to extract the discrete
energy levels of a realistic ring, which are found to agree well with
theoretical expectations. Such an agreement, so far only found for few-electron
quantum dots, is here extended to a many-electron system. In a semiclassical
language our results indicate that electron motion is governed by regular
rather than chaotic motion, an unexplored regime in many-electron quantum dots.
