Definition:Quadrilateral/Rhombus

Definition

A rhombus is a parallelogram whose sides are all the same length.

Its angles may or may not all be equal.

Euclid's Definitions

In the words of Euclid:

Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.

(The Elements: Book $\text{I}$: Definition $22$)

Also known as

A rhombus is also known as a rhomb.

Particularly when it is oriented so that the longer diagonal is a vertical line, a rhombus is often referred to as a diamond.

Some sources give the word lozenge, but this is old-fashioned, and nowadays brings with it an association with throat medication.

Also see

• A square is a rhombus all of whose angles are equal to a right angle.

• A rhombus is a kite all of whose sides are the same length.

• Results about rhombi can be found here.

Linguistic Note

The plural of rhombus is properly rhombi, although you may occasionally see the technically incorrect rhombuses.

The adjectival form of rhombus is rhombic, meaning:

shaped like, or appertaining to, a rhombus.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): parallelogram
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): rhombus, rhomb, diamond or lozenge
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): rhombus (rhomb)
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): rhombus (rhomb)
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): rhombus (rhombi)
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): rhombus (rhombi)