Truncated Dodecahedron
Calculator and formulas for calculating a truncated dodecahedron
This function calculates various properties of a truncated dodecahedron. A truncated dodecahedron is created by cutting off the corners of a dodecahedron so that all edges are the same length. It is a polyhedron with 32 sides, 90 edges and 60 vertices. They form 20 equilateral triangles, 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 Dodecahedron Formulas
Volume \(\small{V}\)
\(\displaystyle V=\frac{5 · a^3 · (99+47 ·\sqrt{5}}{12}\)
Surface \(\small{S}\)
\(\displaystyle S= 5 · a^2 · (\sqrt{3}+6·\sqrt{5+2·\sqrt{5}})\)
Outer radius \(\small{r_c}\)
\(\displaystyle r_c=\frac{a· \sqrt{74+30· \sqrt{5}}}{4}\)
Midsphere radius \(\small{r_m}\)
\(\displaystyle r_m=\frac{a · (5+3·\sqrt{5})}{4} \)
Edge length \(\small{a}\)
\(\displaystyle a= \sqrt[3]{ \frac{12 · V }{5·(99 + 47 ·\sqrt{5})}} \)
\(\displaystyle a= \sqrt{ \frac{S}{5 ·(\sqrt{3}+6·\sqrt{5+2·\sqrt{5})}}} \)
\(\displaystyle a=\frac{4·r_c}{(74+30· \sqrt{5})}\)
\(\displaystyle a=\frac{4 · r_m}{5+3·\sqrt{5}} \)
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