# Definition:Octahedron/Regular

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## Definition

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

It has:

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

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $4$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $5$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $6$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $8$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.4$: Euclid (flourished ca. $300$ B.C.) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $4$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $5$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $6$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $8$ - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Euclid