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.

A rotating tetrahedron

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

References

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

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[Cox-1] Coxeter, Harold Scott MacDonald; Regular Polytopes, Methuen and Co., 1948, Table I(i)

[2] Köller, Jürgen, "Tetrahedron", Mathematische Basteleien, 2001