Golden Rhombus

A golden rhombus is a rhombus whose diagonals are in the ratio , where is the golden ratio.

The faces of the acute golden rhombohedron, Bilinski dodecahedron, obtuse golden rhombohedron, rhombic hexecontahedron, and rhombic triacontahedron are golden rhombi.

The half-angle is given by

			(1)
			(2)
			(3)
			(4)

(OEIS A195693).

Labeling the smaller interior angle as and the larger as , then

(5)

and

			(6)
			(7)
			(8)
			(9)
			(10)
			(11)
			(12)
			(13)
			(14)
			(15)
			(16)
			(17)

(OEIS A105199 and A137218).

The diagonal lengths of a golden rhombus with edge length are given by

			(18)
			(19)
			(20)
			(21)
			(22)
			(23)
			(24)
			(25)

(OEIS A121570 and A179290), the inradius by

(26)

and the area by

(27)