Platonic Solids and the Elements
Platonic Solids and the Elements
By
Roland Matthews (2019)
What is a Platonic solid? In Geometry they are defined as: any regular, congruent, convex polyhedron in three-dimensional space constructed with the same number of faces meeting at each vertex. What does that mean? In order to meet that criteria, all angles and sides must be flat, equal, and identical in shape and size, while fitting within a sphere. The Greek philosopher Plato is given credit for discovering the only five special shapes that meet all the requirements. They are: the tetrahedron, the cube, the octahedron, the dodecahedron, and the icosahedron. Some of our readers may recognize these as the dice used in many popular table top role playing games. In addition, they are each associated with a corresponding element.
The tetrahedron has four triangular sides / faces, six edges, four vertices, and is associated with fire. The cube has six square faces, twelve edges, eight vertices, and is associated with earth. The octahedron has eight triangular faces, twelve edges, six vertices, and is associated with air. The dodecahedron has twelve pentagonal faces, thirty edges, twenty vertices, and is associated with ether / spirit. The icosahedron has twenty triangular faces, thirty edges, twelve vertices, and is associated with water. One peculiar trait that they share is that two polyhedra whose faces and vertices correspond within each other are called duals.[1] For example, an octahedron fits perfectly inside a cube and vice versa. So does a dodecahedron fit exactly inside an icosahedron and vice versa. The tetrahedron is self-dual in that an inverted tetrahedron fits within another tetrahedron.
This dualism would suggest an inverse relationship between the elements of earth and air, and between water and spirit, leaving fire in a unique position. Perhaps this is one reason why the alchemists of old were called fire worshipers. The four faces were also related to the four degrees or levels of heat they used in their experiments. The six faces of the cube represent the solidity of matter which can be symbolized by the six pure shapes when including the sphere with the Platonic solids. Another discussion topic for later will be an in depth look at the Cube of Space, an esoteric teaching from the Sepher Yetzirah, one of the foundational texts of Qabbalah. The eight faces of the octahedron can be related to both the Eastern and Western eight winds. The dodecahedron was also considered to be sacred and related to spirit because the pentagonal faces are associated with the golden ratio or Phi. And since it has twelve faces, it can also be associated with the twelve signs of the zodiac. The twenty faces of the icosahedron could be correlated to the twenty sephiroth of the Tree of Life and its shadow Qlippoth. In addition, there are sixteen elemental court cards and four aces in the lesser arcana of the Tarot, but anything other than this is a mystery and open for comment.
An interesting object known as the stellated octangula can be constructed by interlacing two same size tetrahedrons where one is inverted. It is a three-dimensional Star of David also called the Merkabah. If one connects the vertices of this, it creates a cube. In the center of it is an octahedron, and in the center of that is an icosahedron, whose dual is the dodecahedron which can also be built on the exterior of the cube. An ancient two-dimensional representation of how all these fit within each other is known as Metatron’s Cube.
Another way to compare these elements is through color and sound. In the Western tradition, fire is red and the musical tone C; earth is green and F#, air is yellow and E, water is blue and G#, and spirit is violet and A#. In astrological terms, the duals are sextile to one another. But this is for another discussion.
[1] Sutton, Daud (2002). Platonic & Archimedean Solids. Walker & Co., New York, NY. p. 16.
