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:

$8$ vertices

$12$ edges

$6$ faces

Also known as

The word cube is the common name for regular hexahedron.

Also see

• Definition:Platonic Solid

• 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): $6$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): hexahedron
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): Platonic solid
• 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): $6$
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): cube: 2.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hexahedron
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): cube: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hexahedron
• 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): cube
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): Platonic solid: $\text {(ii)}$