Truncated Octahedron

This function calculates various properties of a truncated octahedron. A truncated octahedron is created from an octahedron where the corners are cut off in such a way that all edges are the same length. To perform the calculation, select the property you know and enter its value. Then click on the 'Calculate' button.

Truncated octahedron calculator  Input Delete Entriy 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 Outerradius rc Midsphere radius rm

Formulas for the truncated octahedron

Volume

\(\displaystyle V= 8· a^3 ·\sqrt{2}\)

\(\displaystyle a= \sqrt[3]{ \frac{ V }{8 ·\sqrt{2}}} \)

Surface area

\(\displaystyle S= 6 · a^2 ·(1+2· \sqrt{3})\)

\(\displaystyle a= \sqrt{ \frac{S}{6·(1+2· \sqrt{3})}} \)

Outer radius

\(\displaystyle rc=\frac{a·\sqrt{10}} {2} \)

\(\displaystyle a=\frac{2·rc}{ \sqrt{10}} \)

Midsphere radius

\(\displaystyle rm=\frac{3·a}{2}\)

\(\displaystyle a= \frac{2 ·rm}{3} \)