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 ${\displaystyle {\frac {\sqrt {2}}{12}}a^{3}}$

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.