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.