In Euclidian geometry it's a point. In non-Euclidean geometry all bets are off.
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Parallel lines in Euclidean space are always coplanar.
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 10 points of intersection.
If no pair of lines is parallel and if each pairwise intersection is distinct, there will be 6 points of intersection.
a point
Parallel lines will be co-planar.