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.

Calculate truncated tetrahedron  Input Delete Entries Edge lenth Volume Surface Outer radius Midsphere radius Decimal places 0 1 2 3 4 6  Results Edge length a Volume V Surface S Outer radius rc Midsphere radius rm

Formulas for the truncated tetrahedron

Volume
\(\displaystyle V=\frac{23 · \sqrt{2} · a^3}{12}\)	\(\displaystyle a= \sqrt[3]{ \frac{12 · V }{23 ·\sqrt{2}}} \)
Surface
\(\displaystyle S= 7 · a^2 · \sqrt{3}\)	\(\displaystyle a= \sqrt{ \frac{S}{7 ·\sqrt{3}}} \)
Outer radius
\(\displaystyle rc=\frac{a · \sqrt{22}}{4} \)	\(\displaystyle a=\frac{4 · rc}{ \sqrt{22}} \)
Midsphere radius
\(\displaystyle rm=\frac{3 · a · \sqrt{2}}{4} \)	\(\displaystyle a=\frac{4 · rm}{3 · \sqrt{2}} \)