Definition:Tetrahedron/Regular

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Definition

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


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.

(The Elements: Book $\text{XIII}$: Proposition $13$)


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.


Sources