The answer depend on the truncation but assuming it is by a plane parallel to the base, the truncated tetrahedron is like a triangular prism (except that one base is smaller than the other). It, therefore, has 5 faces, 6 vertices and 9 edges.
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A tetrahedron has:4 faces4 vertices6 edges
A truncated pyramid has: faces = number_of_edges_round_polygon_of_base + 2 vertices = number_of_edges_round_polygon_of_base x 2 edges = number_of_edges_round_polygon_of_base x 3
A tetrahedron which is a triangular based pyramid has 4 vertices, 4 faces and 6 edges
A triangular based pyramid which is a tetrahedron has 4 faces, 6 edges and 4 vertices
A tetrahedron triangular based pyramid has 6 edges, 4 faces and 4 vertices