Rhombus

In geometry, a rhombus (pl.: rhombi or rhombuses) is an equilateral quadrilateral, a quadrilateral whose four sides all have the same length. Other names for rhombus include diamond, lozenge, and calisson. Every rhombus is a simple polygon (having no self-intersections). A rhombus is a special case of a parallelogram and a kite. A rhombus with right angles is a square. A non-square rhombus has two opposite acute angles and two opposite obtuse angles.

Infobox

Type

quadrilateral, trapezoid, parallelogram, kite

Edges and vertices

Schläfli symbol

{

Symmetry group

Dihedral (D2), , (*22), order 4

Area

}} (half the product of the diagonals)

Properties

convex, isotoxal

Dual polygon

rectangle

Tables

As topological square tilings		As 30-60 degree rhombille tiling

Example polyhedra with all rhombic faces · Other properties › As the faces of a polyhedron

Trigonal trapezohedron

Isohedral

Trigonal trapezohedron

Isohedral

Rhombic dodecahedron

Isohedral golden rhombi

Rhombic triacontahedron

Isohedral golden rhombi

Rhombic icosahedron

2-isohedral

Rhombic enneacontahedron

3-isohedral

Rhombohedron

Isohedral		Isohedral golden rhombi		2-isohedral	3-isohedral

Trigonal trapezohedron	Rhombic dodecahedron	Rhombic triacontahedron	Rhombic icosahedron	Rhombic enneacontahedron	Rhombohedron

References

Euclid's original definition and some English dictionaries' definition of rhombus excludes squares, but modern mathemati
For the Learning of Mathematics
https://www.jstor.org/stable/40248098
Choes and Anthesteria
https://books.google.com/books?id=dcwUAAAAIAAJ&dq=iynx+disc&pg=PA46
"The Origin of Rhombus"
https://web.archive.org/web/20150402143657/http://www.pballew.net/rhomb
A New English Dictionary on Historical Principles
https://archive.org/details/oxforddictionaryv3p1unse_a5h6/page/314/mode/1up
A Mathematical Space Odyssey: Solid Geometry in the 21st Century
https://books.google.com/books?id=2F_0DwAAQBAJ&pg=PA28
Zalman Usiskin and Jennifer Griffin, "The Classification of Quadrilaterals. A Study of Definition Archived 2020-02-26 at
https://books.google.com/books?id=ff0nDwAAQBAJ&q=rhombus
Owen Byer, Felix Lazebnik and Deirdre Smeltzer, Methods for Euclidean Geometry Archived 2019-09-01 at the Wayback Machin
https://books.google.com/books?id=W4acIu4qZvoC&q=rhombus
Paris Pamfilos (2016), "A Characterization of the Rhombus", Forum Geometricorum 16, pp. 331–336, [1] Archived 2016-10-23
http://forumgeom.fau.edu/FG2016volume16/FG201640.pdf
"IMOmath, "26-th Brazilian Mathematical Olympiad 2004""
https://imomath.com/othercomp/Bra/BraMO04.pdf
MathWorld
https://mathworld.wolfram.com/Rhombus.html
de Villiers, Michael, "Equiangular cyclic and equilateral circumscribed polygons", Mathematical Gazette 95, March 2011,