A planar graph has:
12 edges and 6 faces.
Calculate the number of vertices using
Eulers Formula for Planar Geometry
Draw a planar graph
Include zero edge intersections
with v vertices, e edges and f faces
v - e + f = 2
Rearrange Eulers Formula
v = e - f + 2
v = 12 - 6 + 2
v = 6 + 2