An octagonal pyramid.
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Faces=9 Vertices: 9 Edges=16
The shape you are describing is a truncated octahedron. A truncated octahedron is a polyhedron with 16 vertices, 24 edges, and 10 faces. It is created by truncating an octahedron by cutting off its corners, resulting in a shape with hexagonal and square faces.
octagonal prism
It has 8 vertices, 12 edges and 6 faces.
A pyramid with an n-sided base will have n + 1 vertices, n + 1 faces, and 2n edges. 16 edges, 9 vertices