A triangle can have no parallel lines.
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A pentagon has no parallel lines.
A cube has exactly 6 parallel lines.
A cube has exactly 6 parallel lines.
If it is normal, in that it has finite size, then no. parallel lines never meet together in any way The answer is apparently yes, according to non-euclidian geometry. I do not know the specifics, but I am researching it now. It has to do with a triangle inside a sphere.