A golden rhombus is a rhombus

Rhombus

In Euclidean geometry, a rhombus or rhomb is a convex quadrilateral whose four sides all have the same length. The rhombus is often called a diamond, after the diamonds suit in playing cards, or a lozenge, though the latter sometimes refers specifically to a rhombus with a 45° angle.Every...

 whose diagonals are in the ratio , where is the golden ratio

Golden ratio

In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The golden ratio is an irrational mathematical constant, approximately 1.61803398874989...

. The plural of rhombus is rhombi, and a polyhedron

Polyhedron

In elementary geometry a polyhedron is a geometric solid in three dimensions with flat faces and straight edges...

 whose faces are golden rhombi is a golden rhombohedron

Rhombohedron

In geometry, a rhombohedron is a three-dimensional figure like a cube, except that its faces are not squares but rhombi. It is a special case of a parallelepiped where all edges are the same length....

. One such polyhedron is the rhombic triacontahedron

Rhombic triacontahedron

In geometry, the rhombic triacontahedron is a convex polyhedron with 30 rhombic faces. It is an Archimedean dual solid, or a Catalan solid. It is the polyhedral dual of the icosidodecahedron, and it is a zonohedron....

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The internal angles of the rhombus are
The dihedral angle

Dihedral angle

In geometry, a dihedral or torsion angle is the angle between two planes.The dihedral angle of two planes can be seen by looking at the planes "edge on", i.e., along their line of intersection...

 between adjacent rhombi of the rhombic triacontahedron is 144°, which can be constructed by placing the short sides of two golden triangles back-to-back.
The edge length of the golden rhombus with short diagonal is
A golden rhombus with unit edge length has diagonal lengths