Rhombus with diagonals in the golden ratio
In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio:
formula_1
The area of the golden rhombus in terms of its diagonal length formula_4 is:
formula_6
Area.
 ;br ;
The area of the golden rhombus in terms of its edge length formula_7 is:
formula_9
Note: formula_10 , hence: formula_11
As the faces of polyhedra.
Several notable polyhedra have golden rhombi as their faces.
They include the two golden rhombohedra (with six faces each), the Bilinski dodecahedron (with 12 faces),
the rhombic icosahedron (with 20 faces),
the rhombic triacontahedron (with 30 faces), and
the nonconvex rhombic hexecontahedron (with 60 faces). The first five of these are the only convex polyhedra with golden rhomb faces, but there exist infinitely many nonconvex polyhedra having this shape for all of their faces.