Icosahedron Volume Calculator

Work out icosahedron volume instantly with clear inputs, formula shown and shareable results.

About Icosahedron Volume Calculator

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.

Formulas

Volume

V = (5/12)(3 + √5)·a³

Surface area

S = 5√3·a²

Worked example

With the default values below, Icosahedron Volume Calculator returns Volume of 58.9058. Change any input above and every figure here is recalculated in your browser.

Inputs used

Edge lengthminimum 0: 3
Number of solidsminimum 1: 1

Results

Volume: 58.9058
Surface area (20 triangles): 77.9423
Circumradius: 2.8532
Combined volume: 58.9058

Step by step

1Values used
2Volume
3Surface area
4Volume= 58.9058
5Surface area (20 triangles)= 77.9423
6Circumradius= 2.8532
7Combined volume= 58.9058

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

How many faces, edges and vertices?

Twenty faces, thirty edges and twelve vertices: 12 − 30 + 20 = 2.

What is its dual?

The dodecahedron; they share the same symmetry group.