The shape you are describing is a rectangular prism. A rectangular prism has 8 vertices, with each vertex connecting three edges. It also has 6 faces, with each pair of opposite faces being parallel to each other.
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A rectangular prism has six faces, and each pair of opposite faces is parallel to each other. Therefore, a rectangular prism has three pairs of parallel faces.
A cuboid has 3 pairs of parallel faces.
3 pairs
a cube * * * * * It cannot be a cube because a cube does not have 8 pairs of perpendicular faces - it has 12.
A cuboid has 6 faces, and each face has a pair of parallel faces. So, a cuboid has 3 pairs of parallel faces. Mathematically speaking, that's the tea, honey.