There is a sphere and you have to make numerous different three-dimensional forms with these rules:
- You can only use straight lines.
- All these lines must touch the surface of the sphere
- All the lines must be of equal length
- All the shapes made have to be the same
You could make an infinite amount, however since every square has to be of equal length, and all the shapes made had to be the same, you could only produce 5 different “perfect solids”. These are the Platonic Solids, also known as the Pythagorean Solids or the 5 Elements, which consist of:
- Tetrahedron, equated with Fire
- Octahedon, equated with Air
- Hexahedron, equated with Earth
- Icosahedron, equated with Water
- Dodecahedron, equated with Aether (Spirit/World Soul)
The Five Solids, being directly associated as particles of the elements, are seen as the building blocks of reality. By using geometric figures, Pythagoras (and later Plato) implicitly connects the 5 solids to ideas of harmony and symmetry, and as such offer insights into the nature of the cosmos
Tetrahedron – Fire
We can connect three equilateral triangles together to make a point. One more is required to fill in the other side for a total of 4 triangles. This is called the tetrahedron, with Tetra meaning “4” and “hedron” meaning sided, and is the first perfect solid.
Plato associated this solid with Fire because of its pointy ends, which he explained mimic the stabbing sensation of a flame. Furthermore, it’s the simplest and lightest solid. This is the element that is linked to the soul and creates change.
Octahedron – Air
The octahedron symbolizes Air, according the Plato and the other Pythagoreans. The Octahedron, as the name suggests, has 8 triangular sides.
Air particles acts as an intermediate between water-particles and air-particles.
Hexahedron – Earth
The Hexahedron, or the Cube, is the shape of Earth-particles, as the cube is a regular solid that possesses greatest stability, being firmly rooted to its spot. It has 6 square sides.
Icosahedron – Water
While fire-particles are tetrahedral due to being light and simple, the opposite is true for water-particles, which are icosahedral for being heavy and complex. After all, it is something able to easily squash and extinguish a flame. This has 20 triangular sides.
Dodecahedron – Aether
The dodecahedron is the most mysterious of the solids. It’s by far the most difficult to construct; accurate drawing of the regular pentagon requiring a rather elaborate application of Pythagoras’ great theorem, with its 12 pentagonal sides, which leads Plato to conclude that the Dodecahedron is what “the Deity employed in tracing the plan of the Universe.” The Demiurge used this for arranging the constellations of the heavens.
“Numbers are the Highest Degree of knowledge. They are knowledge themselves”
Cohen, S. Marc. Platos Cosmology: The Timaeus. 2006. Accessed December 06, 2017. https://faculty.washington.edu/smcohen/320/timaeus.htm.
“The Platonic and Pythagorean Solids.” √ø∑Dubs. August 27, 2016. Accessed September 08, 2017. http://joedubs.com/the-platonic-and-pythagorean-solids/.
Calter, Paul. Geometry in Art & Architecture Unit 6. 1998. Accessed December 06, 2017. https://www.dartmouth.edu/~matc/math5.geometry/unit6/unit6.html.