# Rhombus

(Redirected from Rhomb)
Rhombus
Rank2
TypeIsotopic
SpaceSpherical
Notation
Bowers style acronymRhomb
Coxeter diagramm2m
Elements
Edges4
Vertices2+2
Measures (edge length 1, angle α)
Inradius${\displaystyle \frac{\sin\alpha}{2}}$
Area${\displaystyle \sin\alpha}$
AnglesAcute: ${\displaystyle \alpha}$
Obtuse: ${\displaystyle \pi-\alpha}$
Height${\displaystyle \sin\alpha}$
Central density1
Related polytopes
ArmyRhomb
RegimentRhomb
DualRectangle
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryK2, order 4
ConvexYes
NatureTame

The rhombus, or rhomb, is a quadrilateral with all four edges of the same length. It has two different angles, and its diagonals are always at right angles. It is a special case of a parallelogram.

The two angles of a rhombus add up to 180°, and one is always acute, the other is obtuse. Rhombi occur as faces in two of the Catalan solids, namely the rhombic dodecahedron and rhombic triacontahedron.

A rhombus can be considered to be the tegum product of two dyads of different lengths. These two dyads then form the two diagonals of the rhombus.

## Golden rhombus[1][2]

The golden rhombus is a rhombus whose diagonals have the golden ratio. It appears as a face of the golden isozonohedra as well as other polyhedra such as the rhombic hexecontahedron.

### Vertex coordinates

The coordinates of a golden rhombus centered at the origin with side lengths equal to 1:

• ${\displaystyle \left(\pm\frac{1}{2}\sqrt{\frac{8}{5+\sqrt{5}}},0\right)}$,
• ${\displaystyle \left(0,\pm\frac{1}{2}\sqrt{2+\frac{2}{\sqrt{5}}}\right)}$.