A pyramid with a hexagon-shaped base has 12 edges, seven faces and seven vertices (points where edges meet). The qualities of a polyhedron are intrinsically related to one another, as is shown using an equation called Euler's polyhedron formula.
Euler's polyhedron formula, named after Leonard Euler (pronounced "oy-ler") and not to be confused the Euler Formula, mathematically shows the relationship between a polyhedron's edges, faces and vertices. It says that the number of faces plus the number of vertices minus the number of edges will always equal two. In the case of a hexagonal pyramid, this equates to seven faces plus seven vertices minus 12 edges equals two.