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No.
A pyramid is a generic name for a polyhedron (solid shape) with one face (the base) which is a polygon with n sides (n ≥ 3), and n triangular faces. It will have n+1 vertices (corners).
Thus,
a triangular pyramid has 4 corners
a quadrilateral pyramid has 5 corners
a pentagonal pyramid has 6 corners, and so on.
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A pyramid has.
A hexagon based pyramid has 7 corners.
If you mean the base has 4 sides then the pyramid is a square based pyramid and has 5 corners. If you mean the pyramid has 4 faces then the pyramid is a tetrahedron with a triangular base and has 4 corners.
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