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Volume of a regular dodecahedron calculator

Enter the dimensions of a regular dodecahedron and read off its volume and surface area. Volumes convert to litres and gallons with the unit selector.

Volume
206.904 21m³
≈ Rounded Volume of a regular dodecahedron
Surface area
185.811 56
Show the working
  1. Edge length = 3
  2. Volume = (15 + 7*sqrt(5)) / 4 * 3^3 = 206.904
  3. Surface area = 3 * sqrt(25 + 10*sqrt(5)) * 3^2 = 185.812

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 = ((15 + 7 sqrt 5)/4) e^3
    • surface area = 3 sqrt(25 + 10 sqrt 5) e^2

    Switch the volume unit to litres or US gallons to read the capacity directly.

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