A square pyramid has one base, and it is a square. That's why it's called a square pyramid. And because the base is a square, it has four sides.
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5 faces do a square pyramid
A rectangular pyramid, or a square pyramid, has 5 faces in all.
A square pyramid will not have any curved faces.
A square pyramid has 5 faces and 5 vertices.
A pyramid can have 0 or 1 square faces. It can have 4 or more faces - there is no limit.