16) Plato particularly loved the regular dodecahedron, which is a polyhedron whose faces are 12 equal regular pentagons. How many edges and vertices does this polyhedron have?
(A) 20 edges and 20 vertices
(D) 30 edges and 60 vertices
(B) 30 edges and 20 vertices
(C) 20 edges and 30 vertices
16) The answer is $(\mathrm{B})$.

Indeed, the sides of the polygons are a total of $12 \cdot 5=60$; since each edge of the polyhedron is common to two faces, there are $\frac{60}{2}=30$ edges of the polyhedron.

At the vertices of the polyhedron, no fewer than three faces can obviously converge, nor more than three (the angle at the vertex of a regular pentagon is $\frac{5-3}{5} 180^{\circ}=108^{\circ}$ and $4 \cdot 108^{\circ}>360^{\circ}$). Therefore, exactly three faces converge at each vertex, and thus the number of vertices is $\frac{60}{3}=20$.