A square has 1 face
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Number of faces on a square pyramid is 5.
A polyhedron can have any number of faces 4 or higher.
Lateral faces are the number of faces excluding the base. Since the square is the base, the other 4 sides will each be touching a lateral face to form a square pyramid (or it wont be a pyramid). So, there are 4.
A square pyramid has four triangular faces and one square face. In total, that is five faces.
A cuboid can have 2, 4 or 6 square faces.