No.
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Yes, a cuboid does have parallel edges. In a cuboid, all pairs of opposite edges are parallel to each other. Additionally, the opposite faces of a cuboid are also parallel to each other.
a cuboid has 12 edges
A cuboid could fit the given description which as 12 edges, 6 faces and 8 vertices
a cuboid has 6 faces, and it has 12 edges.
Why Yes!