The four classical elements of fire, air, earth and water were not only known Greece but ornamented models have been found all that date back to way before Plato or any other Greek philosopher. However, Plato seems to be the first one to refer to them with the word “elements” and he is the one that assigned his Platonic solids to each of them, even though the discovery of these solids is disputed and some authors credit Pythagoras for their discovery.
The Platonic solids were mainly used by Plato and are therefore named after him. The shapes he used were the tetrahedron, the hexahedron or simply cube, the octahedron, the dodecahedron and the icosahedron. These five are the only Platonic solids that exist, which has been explained by mathematical analysis of these solids. The basic principle of a Platonic solid is that all sides are the same shape, i.e. triangles, pentagons, squares, and that the interior angles of the vertexes where the shapes meet add up to less than 360 degrees. There are other shapes, i.e. the Kepler solids or Archimedean solids, however their sides are not uniform as in the Platonic solids.
So why did Plato assign which elements to a certain shape and how did he explain it?
Well the first thing that has to be said is that Plato did come up with another “element” to fit his fifth shape, since there were only four classical elements. He described this fifth element as the element "the god used for arranging the constellations on the whole heaven" (Timaeus 55). Other names from other writers for this element were for example quintessence or aether.
Well the first thing that has to be said is that Plato did come up with another “element” to fit his fifth shape, since there were only four classical elements. He described this fifth element as the element "the god used for arranging the constellations on the whole heaven" (Timaeus 55). Other names from other writers for this element were for example quintessence or aether.
The other four elements were assigned as follows:
Water, the icosahedron: the smoothest and most spherical of all these shapes was to describe the flowing nature of water.
Fire, the tetrahedron:, the sharp edges of this shape were to represent the feeling of touching a fire.
Earth, the hexahedron or cube: this shape is the least smooth of all shapes and describes the brittle and crumbling nature of the dirt that is made of it.
Air, the octahedron: the shape of the octahedron allows movement into any direction without interference and therefore represented air.
And lastly the dodecahedron, the element of the universe as already described above.
There were also many other models of the classical elements in other cultures but in terms of our western world the Greek model did have the biggest influence.
In the 16th century the German astronomer Johannes Kepler tried to find a connection between the five Platonic solids and the other five known planets known at that time.
He then published a paper in which he presented a model in which the five solids were enclosed in one another only divided by a number of spheres which represented the six known planets of that time. The order of the solids was as follow, going from inside to outside: octahedron, icosahedron, dodecahedron, tetrahedron and cube.
This way the solids represented the distance between the different planets inside the solar system. However, Kepler eventually had to abandon this model which however resulted in the model that the orbits of the planets were ellipses, his two laws of orbitals and in the discovery of the Kepler solids.
He then published a paper in which he presented a model in which the five solids were enclosed in one another only divided by a number of spheres which represented the six known planets of that time. The order of the solids was as follow, going from inside to outside: octahedron, icosahedron, dodecahedron, tetrahedron and cube.
This way the solids represented the distance between the different planets inside the solar system. However, Kepler eventually had to abandon this model which however resulted in the model that the orbits of the planets were ellipses, his two laws of orbitals and in the discovery of the Kepler solids.
Besides Keplers discoveries through the Platonic solids these solids have still persisted up until today as the only five solids that meet all the requirements for being such. Therefore, they have an essential value in mathematics. Eventually there have also been viruses which have been discovered which had the exact shape of a regular octahedron for example. Even though this has nothing to do with Plato it is still remarkable that was the one who came up with these essential shapes. Besides that the Platonic solids also have a vital role in modern engineering and architecture for being esthetic but also offering a high stability.
And of course the whole
And of course the whole
of the classical elements eventually evolved into Alchemy which added Sulphur
Sources:
http://en.wikipedia.org/wiki/Archimedean_solid 
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