Double circular cone ($z^2=x^2+y^2$)

The union of the two infinite lateral conical sheets meeting at a common vertex is a double circular cone. The displayed example has axis $z$ and semi-angle $\pi /4$. It is smooth away from the vertex, where its defining gradient is nonzero. A right circular cone truncated on one side is a related bounded solid; this surface includes both axial directions and has no base disks.