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.

Icosidodecahedron calculator  Input Delete Entry Edge length Volume Surface area 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 icosidodecahedron

Volume

\(\displaystyle V=\frac{a^3 · (45+17 ·\sqrt{5}}{6}\)

\(\displaystyle a= \sqrt[3]{ \frac{6 · V }{45 + 17 ·\sqrt{5}}} \)

Surface area

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

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

Outer radius

\(\displaystyle rc=\frac{a·(1+\sqrt{5})}{2}\)

\(\displaystyle a=\frac{2·rc}{(1+\sqrt{5}})\)

Midsphere radius

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

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