Regulus (geometry)
In three-dimensional space, a regulus R is a set of skew lines, every point of which is on a transversal which intersects an element of R only once, and such that every point on a transversal lies on a line of R. The set of transversals of R forms an opposite regulus S. In R 3 {\displaystyle \mathbb {R} ^{3}} the union R ∪ S is the ruled surface of a hyperboloid of one sheet. Any 3 skew lines generates a pair of reguli: The set of lines that intersect all 3 of them sweeps out a quadratic surface.