A nonahedron.
There are many possible configurations: the simplest two to visualise are an octagonal based pyramid and a heptagonal prism.
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Nonahedron
Since it has 9 faces it is a nonahedron. Not sure how many of the thousands of nonahedrons have 6 vertices.
Triangular prism
No 3D shape with FLAT SIDES has exactly 3 faces. 4 is the minimum.
It is a triangular prism that has 6 vertices, 9 edges and 5 faces.