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

(1) |

(2) |

(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.

© 1996-9

1999-05-25