A pyramid can have any polygonal shape for its base. A pyramid with an n-sided polygonal base has n+1 vertices and n+1 faces.
Assuming you're talking about a square pyramid, there are 5 faces and 5 vertices.
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A square pyramid has 5 faces and 5 vertices.
square pyramid has 5 faces, 5 vertices and 8 edges
Octagonal pyramid: 9 faces 16 edges 9 vertices.
A pentagonal pyramid has 6 faces, 6 vertices and 10 edges.
A triangular based pyramid which is a tetrahedron has 4 faces, 6 edges and 4 vertices