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12 faces.

The number of parallel lines will depend on whether or not the prism is regular and right. In a regular right prism there are 10 parallel edges along the "length". 10 parallel lines make 45 pairs (1-2, 1-3, 1-4, ... 2-3, 2-4, ... etc).

Each line at a base has one parallel line at the same base and two at the opposite base. Each such quartet makes 6 pairs of parallel lines and there are 5 such quartets - so 30 pairs of parallel lines in the bases.

That makes a grand total of 75 pairs of parallel lines.

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Q: How many faces have pairs of parallel lines in decagonal prism?
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