There are lots of different types of pyramids but a square based pyramid has 5 faces, 5 corners and 8 edges
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20 edges, 11 vertices (corners) and 11 faces.
A triangular based pyramid is usually called a tetrahedron and it has 4 faces, 6 edges and 4 corners (usually called vertices)
5 faces 9 edges 6 corners
An octagonal pyramid has 9 faces and 14 edges. The base of the pyramid is an octagon with 8 faces, and the pyramid itself has an additional triangular face. The edges consist of the edges of the octagon base and the edges connecting the base to the apex of the pyramid.
By "corners", do you mean vertices or edges?