Icosidodecahedron
Calculator and formulas for calculating an icosidodecahedron
This function calculates various properties of an icosidodecahedron. An icosidodecahedron is a polyhedron with 32 faces, 30 vertices and 60 edges of equal length (12 pentagons and 20 equilateral triangles).
To perform the calculation, select the property you know and enter its value. Then click on the 'Calculate' button.
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Icosidodecahedron formulas
Volume \(\small{V}\)
\(\displaystyle V=\frac{a^3 · (45+17 ·\sqrt{5}}{6}\)
Surface \(\small{S}\)
\(\displaystyle S= a^2 · (5 ·\sqrt{3}+3·\sqrt{25+10·\sqrt{5}})\)
Outer radius \(\small{r_c}\)
\(\displaystyle r_c=\frac{a·(1+\sqrt{5})}{2}\)
Midsphere radius \(\small{r_m}\)
\(\displaystyle r_m=\frac{a · \sqrt{5+2·\sqrt{5}}}{2} \)
Edge length \(\small{a}\)
\(\displaystyle a= \sqrt[3]{ \frac{6 · V }{45 + 17 ·\sqrt{5}}} \)
\(\displaystyle a= \sqrt{ \frac{S}{5 ·\sqrt{3}+3·\sqrt{25+10·\sqrt{5}}}} \)
\(\displaystyle a=\frac{2·r_c}{(1+\sqrt{5}})\)
\(\displaystyle a=\frac{2 · r_m}{\sqrt{5+2·\sqrt{5}}} \)
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