  In this paper, we introduce a natural dynamical analogue of crystalline
order, which we call choreographic order. In an ordinary (static) crystal, a
high degree of symmetry may be achieved through a careful arrangement of the
fundamental repeated elements. In the dynamical analogue, a high degree of
symmetry may be achieved by having the fundamental elements perform a carefully
choreographed dance. For starters, we show how to construct and classify all
symmetric satellite constellations. Then we explain how to generalize these
ideas to construct and classify choreographic crystals more broadly. We
introduce a quantity, called the "choreography" of a given configuration. We
discuss the possibility that some (naturally occurring or artificial) many-body
or condensed-matter systems may exhibit choreographic order, and suggest
natural experimental signatures that could be used to identify and characterize
such systems.
