Golden rhombus

In geometry, a golden rhombus is a rhombus whose diagonals are in the golden ratio:[1] Equivalently, it is the Varignon parallelogram formed from the edge midpoints of a golden rectangle.

[1] Rhombi with this shape form the faces of several notable polyhedra.

The internal supplementary angles of the golden rhombus are:[3] By using the parallelogram law (see the basic properties of the general rhombus):[5] The edge length of the golden rhombus in terms of the diagonal length

Several notable polyhedra have golden rhombi as their 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.