During the reversal of the Sun's polar fields at sunspot maximum, outward extrapolations of magnetograph measurements often predict the presence of two or more current sheets extending into the interplanetary medium, instead of the single heliospheric current sheet (HCS) that forms the basis of the standard "ballerina skirt" picture. By comparing potential-field source-surface models of the coronal streamer belt with white-light coronagraph observations, we deduce that the HCS was split into two distinct structures with circular cross sections during mid-2012. These cylindrical current sheets were centered near the heliographic equator and separated in longitude by roughly 180° a corresponding four-sector polarity pattern was observed at Earth. Each cylinder enclosed a negative-polarity coronal hole that was identifiable in extreme ultraviolet images and gave rise to a high-speed stream. The two current sheet systems are shown to be a result of the dominance of the Sun's nonaxisymmetric quadrupole component, as the axial dipole field was undergoing its reversal during solar cycle 24.