Rhombus

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