If we just multiply the number of faces by the number of edges per face, this will overestimate the number of edges by a factor of $2$ because each edge will be counted twice. Therefore, we need to divide by $2$ at the end: \[\frac{12\times5}{2} = 30\] so there are $30$ edges in a dodecahedron.

Similarly, each face has $5$ vertices, but they are shared by three faces, so the total number of vertices is: \[\frac{12\times5}{3} = 20.\]