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.

Rhombicosidodecahedron calculator  Input Delete Entry Edge length Volume Surface Outer radius Midsphere radius Decimal places 0 1 2 3 4 6  Results Edge length a Volume V Surface area S Outer radius rc Midsphere radius rm

Formulas for the Rhombicosidodecahedron

Volume

\(\displaystyle V=\frac{a^3 · (60 +29 ·\sqrt{5})}{3}\)

\(\displaystyle a= \sqrt[3]{ \frac{3 · V }{(60 +29 ·\sqrt{5})}} \)

Surface area

\(\displaystyle S= a^2 ·(30+5·\sqrt{3} +3 ·\sqrt{25+10·\sqrt{5}})\)

\(\displaystyle a= \sqrt{ \frac{S}{(30+5·\sqrt{3} +3 ·\sqrt{25+10·\sqrt{5}})}} \)

Outer radius

\(\displaystyle rc= \frac{a·\sqrt{11+4·\sqrt{5}}}{2}\)

\(\displaystyle a=\frac{2· rc}{\sqrt{11+4·\sqrt{5}}}\)

Midsphere radius

\(\displaystyle rm= \frac{a·\sqrt{10+4·\sqrt{5}}}{2}\)

\(\displaystyle a=\frac{2· rm}{\sqrt{10+4·\sqrt{5}}}\)