A conical wedge is an ungula obtained by cutting a solid
cone with a plane placed at an angle oblique to its base.

For the special conical wedge obtained from a cone of height and base radius using a cutting plane through a diameter of the cone's base
and inclined with respect to the base with slope , the volume, surface area, and wedge height can be obtained
in closed form. In addition, the flat face lying in the cutting plane has the following
shape for various values of and .