Page "Skew lines" Paragraph 4

A configuration of skew lines is a set of lines in which all pairs are skew.

Two configurations are said to be isotopic if it is possible to continuously transform one configuration into the other, maintaining throughout the transformation the invariant that all pairs of lines remain skew.

Any two configurations of two lines are easily seen to be isotopic, and configurations of the same number of lines in dimensions higher than three are always isotopic, but there exist multiple non-isotopic configurations of three or more lines in three dimensions.

The number of nonisotopic configurations of n lines in R < sup > 3 </ sup >, starting at n = 1, is