[[Image:Plucker's conoid (n=2).jpg|right|thumb|240px|Figure 1. Plücker's conoid with n = 2 .]][[Image:Plucker's conoid (n=3).jpg|right|thumb|240px|Figure 2. Plücker's conoid with n = 3 .]][[Image:Plucker's conoid (n=4).jpg|right|thumb|240px|Figure 3. Plücker's conoid with n = 4 .]] In geometry, Plücker's conoid is a ruled surface named after the German mathematician Julius Plücker. It is also called a conical wedge or cylindroid; however, the latter name is ambiguous, as "cylindroid" may also refer to an elliptic cylinder. Plücker's conoid is the surface defined by the function of two variables: This function has an essential singularity at the origin. By using cylindrical coordinates in space, we can write the above function into parametric equations Thus Plücker's conoid is a right conoid, which can be obtained by rotating a horizontal line about the z-axis with the oscillatory motion (with period 2π) along the segment [–1, 1] of the axis (Figure 4). A generalization of Plücker's conoid is given by the parametric equations where n denotes the number of folds in the surface. The difference is that the period of the oscillatory motion along the z-axis is 2π⁄n . (Figure 5 for n = 3 ) [[File:Plucker conoid (n=2).gif|thumb|480px|Figure 4. Plücker's conoid with n = 2 .]] [[File:Plucker conoid (n=3).gif|thumb|720px|Figure 5. Plücker's conoid with n = 3 ]]