The Platonic Solids are the five shapes that define the symmetry of points in space and are named after Plato. They are the tetrahedron, cube (or hexahedron), octahedron, dodecahedron and icosahedron. These are considered ‘perfect’ shapes because they look the same from every corner point, every surface is identical, and all sides are made of the same shape. The circle or sphere is the master shape. It is the foundation of the five Platonic and 13 Archimedian solids. The greeks associated four shapes of the Platonic solids with the four classical elements: Cube/Earth, Octahedron/Air, Icosahedron/Water; and Tetrahedron/Fire. Plato wrote that the fifth solid, the dodecahedron, “…the god used for arranging the constellations on the whole heaven.” Aristotle added the ethers as a fifth element but had no interest in associating with it Plato’s fifth solid. The 13 Archimedian solids are more complex and have mixed geometries on each shape, as shown in the image. This is a fascinating subject, and I’ve included a list of books at the end of this article for deeper reading.
The Golden Ratio & Golden Rectangle
If you divide a line so the shorter section is to the longer one, as the longer is to the whole line, you have a golden ratio. It’s so simple a child could do it, yet it forms the basis for much of what we see in the macrocosm and microcosm. This golden mean is similar to cell division or fractals, where dividing the ‘parent’ and reproducing a ‘child’ identical to the parent could go on infinitely. This ratio is expressed as a fraction, an irrational number expressed shortened to 1.618… and called phi. It is phi that constructs many forms that are found throughout nature, as seen in the image above. When I hear someone referring to geometry as ‘sacred’, it is easy to see that this serves as the very precise building block and structure for our world.