Everything in nature is born from one of the Platonic solids: 

Named after the ancient Greek philosopher Plato, platonic solids are geometric shapes where the same number of sides meet at each vertex with the same length and angle to create equal forces. They are the only stable structures found in nature. 

The five platonic solids that meet these criteria are:

The tetrahedron which is associated with the element of fire, 

The cube, which is earth

The octahedron, which is air

The dodecahedron, which is the cosmos, 

and lastly, and most complex is the icosahedron, a 20-sided spherical shape which is associated with the element of water.

Buckminster Fuller won the Gold Medal for designing the geodesic dome, the strongest structure known to man from the American Institute of Architects.  

When he designed the geodesic dome, he extrapolated the math from the icosahedron.

He truncated the icosahedron to make a dome.  

By dividing each side of each triangle by 2, he created a 2-frequency dome. Dividing it by three creates a 3-frequency dome and so on… 

In a geodesic dome each pentagon represents the original hub of the main face of the icosahedron. You can determine the frequency of any dome by counting the number of struts between the centers of each pentagon. 

For 2 frequency and higher, the other hubs are hexagons. 

The higher the frequency, the more curved and spherical the dome is.