How many vertices would a hexagonal geodesic dome have if there was one ring of hexagons around the pentagon?

A hexagonal geodesic dome typically consists of a pentagon at the top and hexagons surrounding it. If there is one ring of hexagons around the pentagon, the pentagon contributes 5 vertices, and each of the 6 hexagons adds 6 vertices. However, the vertices at the edges of the hexagons are shared with the pentagon and with adjacent hexagons, so the total number of unique vertices is 12: 5 from the pentagon and 7 from the hexagons (one vertex from each hexagon shared with the pentagon). Thus, the dome would have 12 vertices.