Golden ratio
Golden rhombus

A golden rhombus is a rhombus whose diagonals are in proportion to the golden ratio, most commonly 1: φ {\displaystyle 1:\varphi }. For a rhombus of such proportions, its acute angle and obtuse angles are:

The lengths of its short and long diagonals d {\displaystyle d} and D {\displaystyle D}, in terms of side length a {\displaystyle a} are:

Its area, in terms of a {\displaystyle a},and d {\displaystyle d}:

Its inradius, in terms of side a {\displaystyle a}:

Golden rhombi form the faces of the rhombic triacontahedron, the two golden rhombohedra, the Bilinski dodecahedron, and the rhombic hexecontahedron.
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