The polycons: the sphericon (or tetracon) has found its family

This paper introduces a new family of solids, which we call $\mathit{\text{polycons}}$, which generalise the sphericon in a natural way. The static properties of the polycons are derived, and their rolling behaviour is described and compared to that of other developable rollers such as the oloid and particular polysphericons. The paper concludes with a discussion of the polycons as stationary and kinetic works of art.