# Definition:Cube/Geometry

## Definition

A **cube** is a hexahedron whose $6$ faces are all congruent squares.

In the words of Euclid:

*A***cube**is a solid figure contained by six equal squares.

(*The Elements*: Book $\text{XI}$: Definition $25$)

It has:

## Also known as

The word **cube** is the common name for **regular hexahedron**.

## Also see

- Results about
**cubes**can be found here.

## Historical Note

According to the Pythagorean tradition, the **cube** was the symbol for the element earth.

## Linguistic Note

The word **hexahedron** derives from the Classical Greek:

**hex**(**ἕξ**), meaning**six****hedron**(a form of**ἕδρα**), meaning**base**or**seat**.

The technically correct plural of **hexahedron** is **hexahedra**, but the word **hexahedrons** 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): $6$ - 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): $6$ - 2008: Ian Stewart:
*Taming the Infinite*... (previous) ... (next): Chapter $2$: The Logic Of Shape