Rhombicosidodecahedron
Calculator and formulas for calculating a rhombicosidodecahedron
This function calculates various properties of a rhombicosidodecahedron. A rhombicosidodecahedron is an Archimedean solid. It has 20 regular triangular faces, 30 square faces, 12 regular pentagonal faces, 60 vertices, and 120 edges.
To perform the calculation, select the property you know and enter its value. Then click on the 'Calculate' button.
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Rhombicosidodecahedron Formulas
Volume \(\small{V}\)
\(\displaystyle V=\frac{a^3 · (60 +29 ·\sqrt{5})}{3}\)
Surface \(\small{S}\)
\(\displaystyle S= a^2 ·(30+5·\sqrt{3} +3 ·\sqrt{25+10·\sqrt{5}})\)
Outer radius \(\small{r_c}\)
\(\displaystyle r_c=\frac{a·\sqrt{11+4·\sqrt{5}}}{2}\)
Midsphere radius \(\small{r_m}\)
\(\displaystyle r_m=\frac{a·\sqrt{10+4·\sqrt{5}}}{2}\)
Edge length \(\small{a}\)
\(\displaystyle a= \sqrt[3]{ \frac{3 · V }{(60 +29 ·\sqrt{5})}} \)
\(\displaystyle a= \sqrt{ \frac{S}{(30+5·\sqrt{3} +3 ·\sqrt{25+10·\sqrt{5}})}} \)
\(\displaystyle a=\frac{2· r_c}{\sqrt{11+4·\sqrt{5}}}\)
\(\displaystyle a=\frac{2· r_m}{\sqrt{10+4·\sqrt{5}}}\)
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