Definition:Octahedron/Regular

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Definition

A regular octahedron is an octahedron whose $8$ faces are all congruent equilateral triangles.


It has:

$6$ vertices
$12$ edges
$8$ faces


The regular octahedron is an example of a deltahedron.


Also known as

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


Also see

  • Results about regular octahedra can be found here.


Historical Note

Euclid in The Elements refers to this object just as an octahedron.

In the words of Euclid:

An octahedron is a solid figure contained by eight equal and equilateral triangles.

(The Elements: Book $\text{XI}$: Definition $26$)


According to the Pythagorean tradition, the regular octahedron was the symbol for the element air.


Linguistic Note

The word octahedron derives from the Classical Greek:

octo (ὀκτώ), meaning eight
hedron (a form of ἕδρα), meaning base or seat.


The technically correct plural of octahedron is octahedra, but the word octahedrons can often be found.


Sources