In solid geometry, what do we call two lines that are not parallel and never intersect?

The term used for two lines that are not parallel and never intersect is "skew lines." In three-dimensional space, skew lines are characterized by the fact that they do not lie in the same plane, which is why they don’t intersect even though they are not parallel.

To understand this better, consider the definitions of the other concepts: intersecting lines are those that cross at a point, parallel lines run in the same direction and remain the same distance apart, and perpendicular lines intersect at a right angle. Thus, these definitions highlight the unique nature of skew lines, which maintain a constant distance from each other without ever meeting. This characteristic sets skew lines apart from the other types of lines mentioned in the question.