View source for Rhomboid

{{Short description|Geometrical concept}}
{{about|the two-dimensional figure|the three-dimensional shape|Rhombohedron|the human back muscles|Rhomboid muscles}}
{{more citations needed|date=September 2012}}
{{being merged|dir=to|Parallelogram|date=June 2025}}
{{Infobox polygon
| name        = Rhomboid 
| image       = Parallelogram.svg
| caption     = A rhomboid is a [[parallelogram]] with two edge lengths and no right angles
| type        = [[quadrilateral]], [[trapezoid|trapezium]]
| edges       = 4
| symmetry    = [[Point reflection|C<sub>2</sub>]], [2]<sup>+</sup>, 
| area        = ''b'' × ''h'' (base × height);<br>''ab'' sin ''θ'' (product of adjacent sides and sine of the vertex angle determined by them)
| properties  = [[convex polygon|convex]]}}

Traditionally, in two-dimensional [[geometry]], a '''rhomboid''' is a [[parallelogram]] in which adjacent sides are of unequal lengths and angles are [[Angle#Types of angles|non-right angled]]. 

The terms "rhomboid" and "parallelogram" are often erroneously conflated with each other (i.e, when most people refer to a "parallelogram" they almost always mean a rhomboid, a specific subtype of parallelogram); however, while all rhomboids are parallelograms, not all parallelograms are rhomboids.

A parallelogram with sides of equal length ([[equilateral]]) is called a ''[[rhombus]]'' but not a rhomboid.
A parallelogram with [[right angle]]d corners is a ''[[rectangle]]'' but not a rhomboid. 
A parallelogram is a rhomboid if it is neither a rhombus nor a rectangle.

==History==
[[Euclid]] introduced the term in his ''[[Euclid's Elements|Elements]]'' in Book 1, Definition 22,
{{blockquote|text=''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.'' |sign=Translation from the page of [[David E. Joyce (mathematician)|D.E. Joyce]], Dept. Math. & Comp. Sci., Clark University [http://aleph0.clarku.edu/~djoyce/java/elements/bookI/defI22.html]}}

Euclid never used the definition of rhomboid again and introduced the word [[parallelogram]] in Proposition 34 of Book 1; ''"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.

==Occurrence==

===In biology===
In biology, rhomboid may describe a geometric rhomboid (e.g. the [[rhomboid muscles]]) or a bilaterally-symmetrical [[kite (geometry)|kite-shaped]] or [[rhombus|diamond-shaped]] outline, as in [[Glossary of leaf morphology#Leaf and leaflet shapes|leaves]] or [[cephalopod fin]]s.<ref>{{cite web |url=http://tolweb.org/accessory/Decapodiform_Fin_Shapes?acc_id=2029 |title=Decapodiform Fin Shapes}}</ref>

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

In anatomy, rhomboid-shaped muscles include the [[rhomboid major muscle]] and the [[rhomboid minor muscle]].

==References==
{{reflist}}

==External links==
*{{MathWorld |urlname=Rhomboid |title=Rhomboid}}

{{Polygons}}

[[Category:Types of quadrilaterals]]