Dissection of a Rhombic Triacontahedron, Golden Ratio

#####Dissection of a Rhombic Triacontahedron

The world of polyhedra is full of beauty! If we start with a golden rhombus, whose long and short diagonals have the golden ratio φ {= (sqrt(5)+1)/2 = 1. 618 …}, and extrude at a taper angle of -18°, we get 1/30 of a rhombic triancontahedron with 30 rhombic faces. It has the same structure as the 30-piece lamp shade (refer to figure).

In light of the structural symmetry, we can just mirror it around in a 5-3-5 pattern for a whole triacontahed