Is there any term for 2 straight-lines not touching yet not equidistant?

Question

In basic school mathematics, I was taught that a pair of straight lines could be either parallel (maintain the same distance between each other ie. Not cross, or intersecting (crossing) each other.

But it is very easy to find a third situation, where the 2 straight-lines are NOT maintaining equal-distance throughout their length, yet they are not crossing each other. Such as this:----

This condition could be easily imagined- if in my room I imagine a diagonal along the floor floor from South-East Corner (C) to North-west corner (D); and imagine another line, a diagonal along the ceiling from North-East-Corner (B) to South West Corner. The 2 straight lines obtained would never touch in a real and finite world, yet they are not parallel.

This is only one condition; many other similar conditions exist. Such as this one on a hexagonal prism (such as pencil)

What should I call them? Should I call them parallel? (since they will not cut anywhere)

Answer 1

In 3-d space, if two lines do not cross yet are not parallel, they are called skew. The lines in your 'pencil' example are skew, for instance.

Answer 2

The fact you mentioned:

lines are either parallel or intersecting

Is only true in the second dimension, in the third dimension, it's planes (entire second dimensions) that intersect and parallel. Lines in the third dimension can be "neither", or not intersect or parallel. As @The Count mentioned, these lines are called skew.

This logic applies to any dimension, an object in $n$ dimension is either parallel or intersecting if the dimension we are measuring in $=n+1$, but not if the dimension $\lt n+1$ In your example lines are $1$ dimensional, and you are calculating in the third dimension. because $1+1\lt3$, lines can be skew.