Work out icosahedron volume instantly with clear inputs, formula shown and shareable results.
A regular icosahedron has twenty equilateral triangular faces. Its volume is (5/12)(3 + √5)a³ ≈ 2.181695a³ and its surface area 5√3·a² ≈ 8.660254a².
Volume
V = (5/12)(3 + √5)·a³
Surface area
S = 5√3·a²
Twenty faces, thirty edges and twelve vertices: 12 − 30 + 20 = 2.
The dodecahedron; they share the same symmetry group.