- published: 22 Apr 2007
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In Euclidean geometry, a rhombus (◊), plural rhombi or rhombuses, is a quadrilateral whose four sides all have the same length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal. A rhombus is necessarily convex. The rhombus is often called a diamond, after the diamonds suit in playing cards, or a lozenge, though the latter sometimes refers specifically to a rhombus with a 45° angle.
Every rhombus is a parallelogram, and a rhombus with right angles is a square. (Euclid's original definition and some English dictionaries' definition of rhombus excludes squares, but modern mathematicians prefer the inclusive definition.)
The word "rhombus" comes from the Greek ῥόμβος (rhombos), meaning something that spins, which derives from the verb ρέμβω (rhembō), meaning "to turn round and round". The word was used both by Euclid and Archimedes, who used the term "solid rhombus" for two right circular cones sharing a common base.
A quadrilateral is a rhombus if and only if it is any one of the following:
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