# What is a Geodesic Dome?

A geodesic dome is essentially an approximation of a hemisphere by a series of triangles, mathematically described as a number of points located on the surface of a hemisphere. We group these points into triples, connecting the three points with straight lines which form the edges of the triangles and the bars of the dome, giving it it’s characteristic strength. But how do we know where to locate these points on the hemisphere? How do we know if this structure gives us a reasonable approximation of a hemisphere? How do we build a geodesic dome mathematically knowing nothing about it? The answer lies over two millennia ago in Ancient Greece. The Greeks, being at the forefront of mathematics of their time, researched a number of mathematical phenomena, including various geometries and shapes. Some of these shapes they described in their writings were known as Platonic Solids, named after the Greek philosopher Plato.

They were known as Platonic Solids, as Plato theorised that the five Platonic Solids made up the world that we know, with each of the five platonic solids representing one of the classical elements (fire, water, earth etc). One of these solids, called the icosahedron, forms the foundation for our geodesic dome. The icosahedron is solid that can be constructed from triangles, having 12 vertices, 30 edges, and 20 faces. Each of these vertices lies on the surface of the circumscribed sphere (a mathematical sphere that surrounds the dome and helps us in constructing it), which will later become the hemisphere that our dome will be approximating. The first step from our icosahedron to our dome is to cut the shape, getting us from approximating a sphere to approximating a hemisphere. Where to cut the dome depends on personal preference, and as we will encounter soon, the frequency of the geodesic shape descended from the icosahedron. For the simplest frequency ν=1, a regular icosahedron, we can either cut the shape at the bottom of the first set of triangles from the top point or at the bottom of the next set of triangles. Frequency cut sections of both the top section and bottom section of an icosahedron

The first option gives a flatter dome, while the second options give higher but more vertical walls around the dome. Cutting in the exact middle of the icosahedron cuts our triangles into two pieces, leaving edges unconnected and the resulting design weak and inelegant. Here we come upon one of the fundamentals geodesic dome construction, the frequency of the geodesic dome. As each face of the icosahedron is a triangle, we can choose to subdivide the triangle into smaller triangles. Each face of the original icosahedron is subdivided into multiple triangles

The number of triangles follows from our chosen frequency for the dome. For a frequency ν=1 our original triangles in our icosahedron remain as they were, frequency ν=2 splits each original triangle in the icosahedron into 4 smaller triangles, ν=3 splits it into 9 triangles, and so on and so forth.