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 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,

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.