Only one case of an unfinished ancient sundial can be found in the scientific literature. Found on the Greek island of Delos, it was first reported in 1938, although the sundial was then later considered lost. In our campaign of October 2012, we rediscovered the sundial. Using new and elaborate techniques, we created a 3D model of the sundial, which has enabled us to answer questions concerning its construction principles and the manufacturing processes used. Our first evaluation has revealed that, initially, its creators had intended to construct a cut conical sundial. Its discovery next to a workshop suggests that the sundial was left there in its unfinished state on the destruction of the island’s main town.