# Tetrahedron

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

## Formulas for a regular tetrahedron

A regular tetrahedron is a tetrahedron whose 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 ${\displaystyle {\frac {\sqrt {2}}{12}}a^{3}}$

## Other properties

A regular tetrahedron's faces are all the same, and so are all its edges, as well as its corners. This makes it a regular polyhedron. It is also convex (its faces do not go through one another), which makes it a Platonic solid.

The dual of regular tetrahedron is another regular tetrahedron. This is called being self-dual.

## References

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