Dodecahedron calculator

This function calculates the volume, the surface and the diagonal of a dodecahedron. A dodecahedron is a three-dimensional shape with 12 sides, 30 edges and 20 corners. To calculate it, select the property you know and enter its value. Then click on the 'Calculate' button.

Dodecahedron calculator  Input Delete Entries Side length Volume Surface Diagonal Decimal places 0 1 2 3 4 6 8 10  Results Side length a Volume V Surface S Diagonal d Height h Circumradius Rc Midradius Rm Inradius Ri

Formulas for calculating a dodecahedron

Volume	\(\displaystyle V=\frac{ a^3}{4}·(15+7·\sqrt{5})\)
Surface	\(\displaystyle S= 3 · a^2 · \sqrt{25+10·\sqrt{5}}\)
Circumradius	\(\displaystyle Rc=\frac{a}{4} · \sqrt{3} ·(1+\sqrt{5}) \)
Midradius	\(\displaystyle Rm=\frac{a}{4} · 3 +\sqrt{5} \)
Inradius	\(\displaystyle Ri=\frac{a}{2} · \sqrt{\frac{25+11·\sqrt{5}}{10}} \)
Diagonal	\(\displaystyle d=2 · Rc \)
Height	\(\displaystyle h=2 · Ri \)