Why does the formula for the volume of a rhombic triacontahedron contain $\sqrt{5}$?

66 Views Asked by At

The volume of a rhombic triacontahedron is calculated by utilising the formula: $$V = 4a^3 \sqrt{ 5+2 \sqrt{5}}$$ where $a$ is the length of an edge.

The rhombic triacontahedron is a polyhedron with a thirty faces; it is a Catalan solid and zonohedron.

Could someone kindly provide me with some insight as to why the formula contains $\sqrt{5}$, featured twice?