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	${\displaystyle {\sqrt {3}}a^{2}\,}$
Face area	${\displaystyle {\frac {\sqrt {3}}{4}}a^{2}\,}$
Height	${\displaystyle {\sqrt {\frac {2}{3}}}\,a\,}$ and ${\displaystyle {\frac {\sqrt {6}}{3}}a}$
Volume	${\displaystyle {\frac {a^{3}}{6{\sqrt {2}}}}\,}$ 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

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