Sacred geometry revolves around the belief that through geometric form, one can gain an understanding of the nature of the world around us and the universe as a whole. This system of philosophy began in the time of the Ancient Egyptians and continued to find popularity through the middle ages. Its concepts are based in verifiable mathematics, yet they often extend into the realm of spirituality. I first encountered sacred geometry in the book Nothing in this Book Is True, But It’s Exactly How Things Are, by Bob Frissell. The book gave an interesting overview of many topics, including sacred geometry, yet failed to go into much detail about the subject. I saw this project as an opportunity to gain a better understanding of sacred geometry and to focus in on a specific part of the philosophy. Although the field of sacred geometry is very broad, containing many different topics and concepts, this will focus on one in particular: Metatron’s Cube (additional link) and its relation to the Platonic Solids (additional link).

     One of the key concepts of sacred geometry is the flower of life. Within this figure, through various expansions, contractions, and connections, one can find a blueprint for concepts espoused by Platonic philosophy and even ancient Judaism to be the basis for the universe and life itself (Frissell, Something 197). When considering the flower of life shape, it is important to realize that this is actually a two-dimensional representation of a three-dimensional form. Therefore, these two figures actually represent the same shape:

  
(Alloca 1)

    In the figure on the left, only nineteen of the spheres are visible, but by representing the shape two-dimensionally, one can see that in actuality, there are a total of twenty-seven spheres.

    Through expanding the flower of life shape to contain 125 spheres, one creates a new shape, from which the “fruit of life” can be extracted (from this vantage point, one sees only thirteen spheres in the fruit of life, but in actuality, there are seventeen, with two both in front and behind of the middle sphere). By connecting the middle point of each sphere to the middle point of all others, Metatron’s cube can be found (Allocca 1).

(Click to Enlarge)
(Melchizidek 7)

(Three-Dimensional View of Metatron's Cube)

     Although the shape of Metatron’s cube has it’s own significance in relation to sacred geometry and other forms of philosophy, it is more widely recognized as the basis for deriving the platonic solids, as seen here:

(Click to Enlarge)
(Melchizidek 8)

    The platonic solids are a group of five three-dimensional solid shapes, each containing all congruent angles and sides. Also, if circumscribed with a sphere, all vertexes would touch the edge of the sphere. It was Euclid who would later prove in his book, entitled The Elements, that these are the only five shapes which actually fit this criteria (Weisstein 1).


(Frissell, Something 200)

     In his book, Timaeus, written in approximately 350 BC, Plato first described these solids, linking them to different elements of reality. The tetrahedron, containing four sides, and actually found twice within Metatron’s cube (the star tetrahedron is a combination of two tetrahedrons), is used to represent fire. The cube, containing six sides, and also found twice within Metatron’s cube, represents the earth. The octahedron, containing eight sides, represents the air. The icosahedron, containing twenty sides, represents the water. Finally, the dodecahedron, containing twelve sides, is used to represent the cosmos (Weisstein 1).

     The concept of the entire universe being made up of four basic elements (earth, fire, water, and air) dates back over a hundred years earlier than Plato’s Timaeus, with the work of the Greek philosopher Empedocles, who lived from approximately 493 to 433 BC. He theorized that all matter is made merely of varying combinations and proportions of these elements. It is possible, however, that this concept also existed long before Empedocles ever wrote about it. He was a disciple of Pythagoras, who had also been greatly influenced by the ancient Egyptians, and Empedocles could have, in theory, gotten his information handed down from either of these sources.

     However, it was Plato, who was born six years after Empedocles’ death, who would apply a logical formula to assigning the elements to the Platonic Solids: “Let us assign the cube to earth, for it is the most immobile of the four bodies and most retentive of shape…the least mobile of the remaining figures (icosahedron) to water, the most mobile (tetrahedron) to fire, the intermediate (octahedron) to air” However, this still leaves the dodecahedron, which, according to Plato, “the god used for embroidering the constellations on the whole heaven" (Calter 2-6). In this way, the Platonic Solids can be used to represent the entire universe. Other shapes within sacred geometry continue to expand upon these principles and provide valuable insight into the nature of all things, from mankind to the cosmos.

     The most difficult part of this project was narrowing such a broad original topic like sacred geometry into a more specific subject such as Metatron’s Cube and the Platonic Solids. However, I am glad that I was able to do a large amount of general research before specifying because this way of doing things allowed me to increase my own knowledge on the subject of sacred geometry. I would definitely like to continue research on the subject in many other areas. Specifically, in my research I found some information linking parts of sacred geometry to ancient Jewish beliefs, and I would like to find out more about this connection. Although it may have seemed a daunting task at first, to gain a complete understanding of sacred geometry, the realization that I still have so much to learn is comforting in that this interesting topic will be able to stay with me for a long time.