There is no regular polyhedron with 9 vertices There are many other defined polyhedra with 9 vertices, though:
elongated square pyramid (cube with a square pyriamd on top)
gyroelongated square pyramid
triangular cupola
triaugmented triangular prism
tridiminished icosahedron
It's hard to describe the shape of some of these. See the related links below for pictures.
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A polyhedron must have at least 4 faces, at least 4 vertices and at least 6 edges.
an elongated square pyramid- here is a website with pictures(http://en.wikipedia.org/wiki/Elongated_square_pyramid )
eighthedron eighthedron
Such a polyhedron cannot exist. According to the Euler characteristics, V + F - E = 2, where V = vertices, F = faces, E = edges. This would require that the polyhedron had only two faces.
Any integer that is greater than 3.