Rhombus

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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 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[edit | edit source]

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 | edit source]

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

  • ,
  • .

References[edit | edit source]

External links[edit | edit source]