Golden rhombus
In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio: Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle. Rhombi with this shape form the faces of several notable polyhedra. The golden rhombus should be distinguished from the two rhombi of the Penrose tiling, which are both related in other ways to the golden ratio but have different shapes than the golden rhombus. Angles (See the characterizations and the basic properties of the general rhombus for angle properties.) The internal supplementary angles of the golden rhombus are: Acute angle: ; by using the arctangent addition formula (see inverse trigonometric functions): Obtuse angle: which is also the dihedral angle of the dodecahedron. Note: an "anecdotal" equality: Edge and diagonals By using the parallelogram law (see the basic properties of the general rhombus): The edge length of the golden rhombus in terms of the diagonal length is: Hence: The diagonal lengths of the golden rhombus in terms of the edge length are: Area By using the area formula of the general rhombus in terms of its diagonal lengths and : The area of the golden rhombus in terms of its diagonal