From an aircraft, a short distinct vertical structure is sometimes seen above the setting sun. Such a feature can be understood as a halo, which is the counterpart of the well-known subsun. Whereas the latter arises from reflections off basal faces of plate-oriented ice crystals illuminated from above, what we call the supersun emerges when these crystals are illuminated from below. The supersun occurs when the sun is below the true horizon and is only visible from elevated positions. The curvature of the Earth causes the ensemble of reflecting crystal faces to act as a hollow mirror and the supersun appears as a vertical band of uniform width, extending from the sun upwards to its supersolar point. We discuss the geometrical properties of the phenomenon and simulate its shape and radiance distribution with an extended version of an atmospheric ray-tracing program.