Rhomboid

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These shapes are rhomboids

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.

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.

—Translation from the page of D.E. Joyce, Dept. Math. & Comp. Sci., Clark University [1]

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[edit]

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

In biology[edit]

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[edit]

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.

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