Truncated Cube

This function calculates various properties of a truncated cube. A truncated hexahedron is created from a cube 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 cube calculator  Input Delete Entry Edge length Volume Surface Height Outer radius Midsphere radius Decimal places 0 1 2 3 4 6  Results Edge length a Volume V Surface area S Height S Outer radius rc Midsphere radiusrm

Formulas for the truncated hexahedron

Volume

\(\displaystyle V=\frac{a^3 ·(21+14* \sqrt{2})}{3}\)

\(\displaystyle a= \sqrt[3]{ \frac{3 · V }{21 + 14 ·\sqrt{2}}} \)

Surface area

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

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

Height

\(\displaystyle h=a·( 1+ \sqrt{2})\)

\(\displaystyle a= \frac{h}{1+ \sqrt{2} } \)

Outer radius

\(\displaystyle rc=\frac{a·\sqrt{7+4· \sqrt{2}}} {2} \)

\(\displaystyle a=\frac{2·rc}{\sqrt{7+4 · \sqrt{2}}} \)

Midsphere radius

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

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