# Rhomboid

Traditionally, in two-dimensional geometry, a **rhomboid** is a parallelogram in which adjacent sides are of unequal lengths and angles are non-right angled.

A parallelogram with sides of equal length (equilateral) is a rhombus but not a rhomboid.

A parallelogram with right angled corners is a rectangle but not a rhomboid.

The term *rhomboid* is now more often used for a rhombohedron or a more general parallelepiped, a solid figure with six faces in which each face is a parallelogram and pairs of opposite faces lie in parallel planes. Some crystals are formed in three-dimensional rhomboids. This solid is also sometimes called a rhombic prism. The term occurs frequently in science terminology referring to both its two- and three-dimensional meaning.

## History

Euclid introduced the term in his *Elements* in Book I, Definition 22,

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 and angles equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.

Euclid never used the definition of rhomboid again and introduced the word parallelogram in Proposition 31 of Book I; *"In parallelogrammic areas the opposite sides and angles are equal to one another, and the diameter bisects the areas."* Heath suggests that rhomboid was an older term already in use.

## Symmetries

The rhomboid has no line of symmetry, but it has rotational symmetry of order 2.

## In biology

In biology, rhomboid may describe a geometric rhomboid (e.g. the rhomboid muscles) or a bilaterally-symmetrical kite-shaped or diamond-shaped outline, as in leaves^{[1]} or cephalopod fins.^{[2]}

## In medicine

In a type of arthritis called pseudogout, crystals of calcium pyrophosphate dihydrate accumulate in the joint, causing inflammation. Aspiration of the joint fluid reveals rhomboid-shaped crystals under a microscope.