Truncated Tetrahedron
Calculator and formulas for calculating a truncated tetrahedron
This function calculates various properties of a truncated tetrahedron. A truncated tetrahedron is a tetrahedron with the corners truncated so 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 Tetrahedron Formulas
Volume \(\small{V}\)
\(\displaystyle V=\frac{23 · \sqrt{2} · a^3}{12}\)
Surface \(\small{S}\)
\(\displaystyle S= 7 · a^2 · \sqrt{3}\)
Outer radius \(\small{r_c}\)
\(\displaystyle r_c=\frac{a · \sqrt{22}}{4} \)
Midsphere radius \(\small{r_m}\)
\(\displaystyle r_m=\frac{3 · a · \sqrt{2}}{4} \)
Edge length \(\small{a}\)
\(\displaystyle a= \sqrt[3]{ \frac{12 · V }{23 ·\sqrt{2}}} \)
\(\displaystyle a= \sqrt{ \frac{S}{7 ·\sqrt{3}}} \)
\(\displaystyle a=\frac{4 · r_c}{ \sqrt{22}} \)
\(\displaystyle a=\frac{4 · r_m}{3 · \sqrt{2}} \)
|
|