Great Dodecahedron Calculator

This function calculates properties of a great dodecahedron.

To perform the calculation select the property you know and enter its value. Then click on 'Calculate'.

Great Dodecahedron Calculator  Input Delete Entry Edge length a Side length s Volume Surface Circle radius Pyramid height Decimal places 0 1 2 3 4 6   Results Edge length a Side length s Volume V Surface area S Circle radius r Pyramid height h

Formulas for calculating a large dodecahedron

Edge length	\(\displaystyle s = \frac{a}{2} \cdot (\sqrt{5} - 1 )\) \(\displaystyle \;\;\; ≈ a \cdot 0.618\)
Volume	\(\displaystyle V=\frac{5}{4}\cdot a^3 \cdot (\sqrt{5} - 1)\) \(\displaystyle \;\;\; ≈ a^3 \cdot 1.545 \)
Surface area	\(\displaystyle S= 15\cdot a^2 \cdot \sqrt{5 - 2\cdot \sqrt{5}}\) \(\displaystyle \;\;\; ≈ a^2 \cdot 10.9 \)
Circumsphere radius	\(\displaystyle r=\frac{a}{4} \cdot \sqrt{10 + 2\cdot \sqrt{5}})\) \(\displaystyle \;\;\; ≈ a \cdot 0.951\)
Pyramid height	\(\displaystyle h = \frac{a}{6} \cdot \sqrt{3} \cdot (3 - \sqrt{5})\) \(\displaystyle \;\;\; ≈ a \cdot 0.221 \)