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.

Rhombus
Rank2
TypeIsotopic
Notation
Bowers style acronymRhomb
Coxeter diagramm2m
Elements
Edges4
Vertices2+2
Vertex figureDyad
Measures (edge length 1, angle α)
Inradius
Area
AnglesAcute:
 Obtuse:
Height
Central density1
Related polytopes
ArmyRhomb
RegimentRhomb
DualRectangle
ConjugateNone
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryK2, order 4
ConvexYes
NatureTame

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 edit

The golden rhombus[1][2] 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 edit

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

  •  ,
  •  .

References edit

External links edit