Work out dodecahedron volume instantly with clear inputs, formula shown and shareable results.
A regular dodecahedron has twelve regular pentagonal faces. Its volume is ((15 + 7√5)/4)a³ ≈ 7.663119a³ and its surface area 3√(25 + 10√5)·a² ≈ 20.645729a².
Volume
V = ((15 + 7√5)/4)·a³
Surface area
S = 3√(25 + 10√5)·a²
Twelve faces, thirty edges and twenty vertices: 20 − 30 + 12 = 2.
Regular pentagons involve the golden ratio (1 + √5)/2, so √5 shows up throughout the dodecahedron's metrics.