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Wallis's conical edge is a ruled surface given by the parametric equations:

$$x=v\cos u,\quad y=v\sin u,\quad z=c\sqrt{a^2-b^2\cos^2u}.\,$$

where a, b and c are constants.

Wallis's conical edge is also a kind of right conoid.

Figure 1. Wallis's Conical Edge with a=b=c=1

Figure 2 shows that the Wallis's conical edge is generated by a moving line.

Wallis's conical edge is named after the English mathematician John Wallis, who was one of the first to use Cartesian methods to study conic sections.[1]

Ruled surface
Right conoid