# Definition:Tetrahedron/Regular

## Definition

A regular tetrahedron is a tetrahedron whose $4$ faces are all congruent equilateral triangles.

It has:

$4$ vertices
$6$ edges
$4$ faces

The regular tetrahedron is an example of a deltahedron.

## Also known as

It is commonplace for authors to refer to a regular tetrahedron as just a tetrahedron, glossing over the fact of its regularity.

## Also see

• Results about regular tetrahedra can be found here.

## Historical Note

The concept of a regular tetrahedron is not mentioned explicitly by Euclid in The Elements.

The first reference to it is in Proposition $13$ of Book $\text{XIII}$: Construction of Regular Tetrahedron within Given Sphere:

In the words of Euclid:

To construct a pyramid, to comprehend it in a given sphere, and to prove that the square on the diameter of the sphere is one and a half times the square on the side of the pyramid.

According to the Pythagorean tradition, the regular tetrahedron was the symbol for the element fire.

## Linguistic Note

The word tetrahedron derives from the Classical Greek τετράεδρόν:

tetrás (τετράς), meaning four
hedron (a form of ἕδρα), meaning base or seat.

The technically correct plural of tetrahedron is tetrahedra, but the word tetrahedrons can often be found.