Truncated Icosidodecahedron
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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Truncated Icosidodecahedron Formulas
Volume \(\small{V}\)
\(\displaystyle V=a^3 (95+50·\sqrt{5}) \) \(\displaystyle \ \ \ ≈a^3 · 206.8033989\)
Surface \(\small{S}\)
\(\displaystyle S= a^2 · 30 \left(1 +\sqrt{3}+\sqrt{5+2·\sqrt{5}}\right)\) \(\displaystyle \ \ \ ≈ a^2 · 174.2920303 \)
Outer radius \(\small{r_c}\)
\(\displaystyle r_c=\frac{a}{2}·\sqrt{31+12·\sqrt{5}}\)
Midsphere radius \(\small{r_m}\)
\(\displaystyle r_m=\frac{a}{2}·\sqrt{30+12·\sqrt{5}}\)
Edge length \(\small{a}\)
\(\displaystyle a = \sqrt[3]{\frac{V}{95+50·\sqrt{5}}} \)
\(\displaystyle a=\sqrt{\frac{S}{30\cdot (1 +\sqrt{3}+\sqrt{5+2\cdot\sqrt{5}})}}\)
\(\displaystyle a=\frac{2· r_c}{\sqrt{31+12·\sqrt{5}}}\)
\(\displaystyle a=\frac{2· r_m}{\sqrt{30+12·\sqrt{5}}}\)
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