Biscribed Truncated Icosahedron(extreme distribution). Vertices 60.
By an extreme distribution of vertices on a sphere, we mean a distribution in which each vertex is the geometric median of the other remaining vertices.
Comparison of properties of three polyhedra
Biscribed Truncated Icosahedron, biscribed form
Vertices: 60 (60[3])
Faces: 32 (12 regular pentagons + 20 ditrigons)
Edges: 90 (30 short + 60 long)
Truncated Icosahedron, canonical form
Vertices: 60 (60[3])
Faces: 32 (12 regular pentagons + 20 regular hexagons)
Edges: 90