# Definition:Icosahedron/Regular

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## Definition

A **regular icosahedron** is an icosahedron whose $20$ faces are all congruent equilateral triangles.

The **regular icosahedron** is an example of a deltahedron.

## Also known as

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

## Also see

- Results about
**regular icoashedra**can be found here.

## Historical Note

In *The Elements*, this object is referred to just as an **icosahedron**.

In the words of Euclid:

*An***icosahedron**is a solid figure contained by twenty equal and equilateral triangles.

(*The Elements*: Book $\text{XI}$: Definition $27$)

According to the Pythagorean tradition, the **regular icosahedron** was the symbol for the element water.

## Linguistic Note

The word **icosahedron** derives from the Classical Greek **εἰκοσάεδρον**:

**eíkosi**(**εἴκοσι**), meaning**twenty****hedron**(a form of**ἕδρα**), meaning**base**or**seat**.

The technically correct plural of **icosahedron** is **icosahedra**, but the word **icosahedrons** can often be found.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $5$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $8$ - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $30$ - 1989: Ephraim J. Borowski and Jonathan M. Borwein:
*Dictionary of Mathematics*... (previous) ... (next): Entry:**icosahedron** - 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): $5$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $8$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $30$ - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic of Shape: Euclid - 2014: Christopher Clapham and James Nicholson:
*The Concise Oxford Dictionary of Mathematics*(5th ed.) ... (previous) ... (next): Entry:**Platonic solid**: $\text {(v)}$