Tetrahedron

A rotating 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	$\sqrt{3}{a}^2$
Face area	$\frac{\sqrt{3}}{4}{a}^2$
Height	$\sqrt{\frac{2}{3}}a$ and $\frac{\sqrt{6}}{3}a$
Volume	$\frac{a^3}{6\sqrt{2}}$ and $\frac{\sqrt{2}}{12}{a}^3$

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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