# Tetrahedron

A rotating tetrahedron

A tetrahedron (triangular pyramid) is a three-dimensional shape. It has four corners. It looks like a pyramid. It has six equally long edges, four corners and four equilateral triangular faces. Every two edges meet on one of those corners forming a sixty-degree angle. All of its sides are triangles.

## Formulas for a regular tetrahedron

A regular tetrahedron is a tetrahedron where all of its edges are the same length. If the length of an edge is a:

 Surface area[1] ${\displaystyle {\sqrt {3}}a^{2}\,}$ Face area ${\displaystyle {\frac {\sqrt {3}}{4}}a^{2}\,}$ Height[2] ${\displaystyle {\sqrt {\frac {2}{3}}}\,a\,}$ and ${\displaystyle {\frac {\sqrt {6}}{3}}a}$ Volume[1] ${\displaystyle {\frac {a^{3}}{6{\sqrt {2}}}}\,}$ and ${\displaystyle {\frac {\sqrt {2}}{12}}a^{3}}$

## References

1. Coxeter, Harold Scott MacDonald; Regular Polytopes, Methuen and Co., 1948, Table I(i)
2. Köller, Jürgen, "Tetrahedron", Mathematische Basteleien, 2001