Calculator and formulas for calculating a 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.
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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
\(\displaystyle rm=\frac{a}{2}·\sqrt{30+12·\sqrt{5}}\)
\(\displaystyle a=\frac{2· rm}{\sqrt{30+12·\sqrt{5}}}\)
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