n=12; as Truncated Tetrahedron
Vertices: 12 (12[3])
Faces: 8 (4 equilateral triangles + 4 regular hexagons)
Edges: 18
The extreme distribution was obtained by me in the applet - "Truncated Tetrahedron. Dependence of the average distance between the vertices of a polyhedron on the truncation parameter. Extreme distribution". Maximization of the average distance between the vertices was performed using truncation parameter.
Information: Truncated Tetrahedron, n=12. Polyhedra with extreme distribution of equivalent vertices.