Truncated Cube
Calculator and formulas for calculating a 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.
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Truncated Cube Formulas
Volume \(\small{V}\)
\(\displaystyle V=\frac{a^3 ·(21+14* \sqrt{2})}{3}\)
Surface \(\small{S}\)
\(\displaystyle S= 2 · a^2 ·(6+6· \sqrt{2} +\sqrt{3})\)
Height \(\small{h}\)
\(\displaystyle h=a·( 1+ \sqrt{2})\)
Outer radius \(\small{r_c}\)
\(\displaystyle r_c=\frac{a·\sqrt{7+4· \sqrt{2}}} {2} \)
Midsphere radius\(\small{r_m}\)
\(\displaystyle r_m=\frac{a·(2+ \sqrt{2})}{2}\)
Edge length \(\small{a}\)
\(\displaystyle a= \sqrt[3]{ \frac{3 · V }{21 + 14 ·\sqrt{2}}} \)
\(\displaystyle a= \sqrt{ \frac{S}{2 ·(6+6· \sqrt{2} +\sqrt{3})}} \)
\(\displaystyle a= \frac{h}{1+ \sqrt{2} } \)
\(\displaystyle a=\frac{2·r_c}{\sqrt{7+4 · \sqrt{2}}} \)
\(\displaystyle a= \frac{2 ·r_m}{2+ \sqrt{2} } \)
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