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Formula Dodecahedron Volume    Side length

Formula
Formula: Dodecahedron
Dodecahedron and its Side Length

Volume

Unit
Volume of a dodecahedron. A regular dodecahedron consists of 12 pentagonal equal faces. The prefactor is approximate:$$ \frac{15 ~+~ 7 \, \sqrt{5}}{4} ~\approx~ 7.66 $$

Side length

Unit
Side length of one side of the pentagon. Since it is a regular polyhedron, all side lengths of a dodecahedron are equal.

For example, with a side length of \( a = 2 \, \text{m} \), the volume of the dodecahedron is:$$ 7.66 \cdot (2 \, \text{m})^3 ~=~ 15.32 \, \text{m}^3 $$