Polyhedron with twelve faces.

A regular dodecahedron is a regular convex polyhedron whose faces are congruent regular pentagons. It is one of the five Platonic solids. It has 20 vertices, 30 edges and 12 faces.

### Formulas

When the length a of the edge of the dodecahedron is given, the volume *V* and total area *A* can be calculated using the following formulas:

\(\mathit{A}=3\sqrt{25+10\sqrt{5}}a^{2}\)

\(\mathit{V}=\frac{15+7\sqrt{5}}{4}a^{3}\)