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
Three skew lines determine a regulus:
- The locus of lines meeting three given skew lines is called a regulus. Gallucci's theorem shows that the lines meeting the generators of the regulus (including the original three lines) form another "associated" regulus, such that every generator of either regulus meets every generator of the other. The two reguli are the two systems of generators of a ruled quadric.
- H. S. M. Coxeter (1969) Introduction to Geometry, page 259, John Wiley & Sons
- Charlotte Angas Scott (1905) The elementary treatment of the conics by means of the regulus, Bulletin of the American Mathematical Society 12(1): 1–7
- Albrecht Beutelspacher & Ute Rosenbaum (1998) Projective Geometry, page 72, Cambridge University Press ISBN 0-521-48277-1
- W. L. Edge (1954) "Geometry of three dimensions over GF(3)", Proceedings of the Royal Society A 222: 262–86 doi:10.1098/rspa.1954.0068
- H. G. Forder (1950) Geometry, page 118, Hutchinson's University Library.