Platonic Solids

Plato, nothing at all like Mickey Mouse's dog.Plato: you have to love this guy. Philosopher, scientist, mathematician… and wrestler… whose name might actually be a nickname given to him by his wrestling coach on account of his broad forehead, though perhaps more likely his shoulders (in Greek "Platon" means broad). You couldn't make this stuff up: it's pure gold. :-)

Anyway, on to the serious stuff:

Equilateral Triangle, Square and Pentagon.

Regular 2D shapes - "regular" means that all sides and angles are the same. So the first is an equilateral triangle. Then we have squares (4 sides), pentagons (5), hexagons (6), heptagons (7), octagons (8), and so on for as long as you like. There's no end to them... although they do get to look more and more like circles as you approach infinity.

Regular solids however i.e. 3D shapes, are a different matter.

Take 4 equilateral triangles, join them together to make a solid and you have a tetrahedron (4 sides). Using 6 squares you can make a cube. Go back to the triangles and with 8 you can make an Octahedron. 12 pentagrams can be used to make a dodecahedron, and 20 triangles can be used to make a icosahedron, which has decided the fate of may a Dungeons and Dragons player in the form of the infamous 20 sided gaming die: the d20.

Crystals, one for each of the platonic solids.

And that's your lot, there are only 5 possible regular solids, and they are named "Platonic Solids" because they are prominent in Plato's philosophy.

[product=EAFW-01A|My Platonic Alchemy Pendant (click for more info)]In the dialogue Timaeus c.360 B.C. Plato associates each of the four classical elements (earth, air, water, and fire) with a regular solid. Earth is associated with the cube, air with the octahedron, water with the icosahedron, and fire with the tetrahedron.

There is intuitive justification for these associations: the heat of fire feels sharp and stabbing (like little tetrahedra). Air is made of the octahedron; its minuscule components are so smooth that one can barely feel it. Water, the icosahedron, flows out of one's hand when picked up, as if it is made of tiny little balls. By contrast, a highly nonspherical solid, the hexahedron (cube) represents "earth". These clumsy little solids cause dirt to crumble and break when picked up in stark difference to the smooth flow of water. Moreover, the cube's being the only regular solid that tessellates (joins to others of it's kind without gaps), was thus believed to cause the solidity of the Earth.

With regard to the fifth Platonic solid, the dodecahedron, Plato obscurely remarks that it was this solid that "...the god used for arranging the constellations on the whole heaven". Aristotle, Plato's most famous student, later added a fifth element, aithêr (aether in Latin, "ether" in English) and postulated that the heavens were made of this element. Aristotle had no interest in matching it with Plato's fifth solid, but a relationship seems apparent.

Kepler's model of the Solar system with close up of the inner part.It is also worth noting that the 16th century German astronomer, Johannes Kepler attempted to relate the five extraterrestrial planets known at that time to the five Platonic solids. In a nutshell: Kepler believed that there was a relationship between distances between the orbits of the planets and the dimensions that a set of Platonic solids would need to be to fit one inside the other.

Of course we now know that Kepler's theory does not hold up, and the concept of four, or five elements, has been superseded by modern science. However I believe that they still have merit.

At school in the 1970s and 80s, I was taught that there were three states in which matter could exist (solid, liquid, and gas), and that atoms were made up of protons, neutrons, and electrons (Atoms were originally called "atoms" because it was believed that they could not be broken down into smaller parts; that's what the word "atom" means).

As I write in 2017, science recognises a fourth state (plasma), and there are more sub-atomic particles defined by modern science than I care to shake a stick at. There is speculation that matter might be just another form of energy, and as anybody with even the slightest knowledge of Descates' philosophy will tell you: you can't prove that any of this "stuff" exists outside of your own imagination anyway… it could all be a dream!

Elements arranged at the points of a pentagram.My point is that all of these things are just models, a means of explaining stuff that we STILL don't fully understand. The purpose of a model is to explain a thing well enough for us to be able to use it, until one day, maybe, the ultimate truth is found.

So if placing crystals, fashioned after the Platonic solids, at the corresponding points of a pentagram, and maybe even relating them to the planets, aids meditation and spell casting, then does it really matter if the model is pooh-poohed by modern science; whose own current best model is just that: its CURRENT BEST MODEL?

Pluto, nothing at all like a Greek philosopher.