# Formula Dodecahedron Volume Side length

## Volume

`$$ V $$`Unit

`$$ \mathrm{m}^3 $$`

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

`$$ a $$`Unit

`$$ \mathrm{m} $$`

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:`$$ 7.66 \cdot (2 \, \text{m})^3 ~=~ 15.32 \, \text{m}^3 $$`