## Plücker's Conoid

A Ruled Surface sometimes also called the Cylindroid. von Seggern (1993) gives the general functional form as

 (1)

whereas Fischer (1986) and Gray (1993) give
 (2)

A polar parameterization therefore gives
 (3) (4) (5)

A generalization of Plücker's conoid to folds is given by

 (6) (7) (8)

(Gray 1993). The cylindroid is the inversion of the Cross-Cap (Pinkall 1986).

References

Fischer, G. (Ed.). Mathematical Models from the Collections of Universities and Museums. Braunschweig, Germany: Vieweg, pp. 4-5, 1986.

Gray, A. Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 337-339, 1993.

Pinkall, U. Mathematical Models from the Collections of Universities and Museums (Ed. G. Fischer). Braunschweig, Germany: Vieweg, p. 64, 1986.

von Seggern, D. CRC Standard Curves and Surfaces. Boca Raton, FL: CRC Press, p. 288, 1993.