Truncated Icosidodecahedron

This function calculates various properties of a truncated icosidodecahedron. A truncated icosidodecahedron has 62 faces; 30 squares, 20 regular hexagons, and 12 regular decagons.

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

Truncated icosidodecahedron calculator  Input Delete Entry Edge length Volume Surface Outer radius Midsphere radius Decimal places 0 1 2 3 4 6  Results Edge length a VolumeV Surface areaS Outer radius rc Midsphere radius rm

Formulas for the truncated icosidodecahedron

Volume

\(\displaystyle V=a^3 (95+50·\sqrt{5}) \)

\(\displaystyle ≈a^3 · 206.8033989\)

\(\displaystyle a = \sqrt[3]{\frac{V}{95+50·\sqrt{5}}} \)

Surface area

\(\displaystyle S= a^2 · 30 \left(1 +\sqrt{3}+\sqrt{5+2·\sqrt{5}}\right)\)

\(\displaystyle ≈ a^2 · 174.2920303 \)

\(\displaystyle a=\sqrt{\frac{S}{30 \left(1 +\sqrt{3}+\sqrt{5+2·\sqrt{5}}\right)}}\)

Outer radius

\(\displaystyle rc=\frac{a}{2}·\sqrt{31+12·\sqrt{5}}\)

\(\displaystyle a=\frac{2· rc}{\sqrt{31+12·\sqrt{5}}}\)

Midsphere radius

\(\displaystyle rm=\frac{a}{2}·\sqrt{30+12·\sqrt{5}}\)

\(\displaystyle a=\frac{2· rm}{\sqrt{30+12·\sqrt{5}}}\)