Volume of a regular icosahedron calculator
Enter the dimensions of a regular icosahedron and read off its volume and surface area. Volumes convert to litres and gallons with the unit selector.
Volume
58.905 765m³
- Surface area
- 77.942 286
Show the working
- Edge length = 3
- Volume = 5 * (3 + sqrt(5)) / 12 * 3^3 = 58.9058
- Surface area = 5 * sqrt(3) * 3^2 = 77.9423
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- volume = (5(3 + sqrt 5)/12) e^3
- surface area = 5 sqrt 3 e^2
Switch the volume unit to litres or US gallons to read the capacity directly.
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