- What Are the Platonic Solids, Exactly?
- Where Metatron’s Cube Comes From
- How the Five Solids Fit Inside the Thirteen Circles
- Why This Relationship Mattered to the Kabbalists
- What the Renaissance Magicians Did With It
- The Mathematical Objectivity Behind the Symbolism
- What People Get Wrong About This Diagram
- How to Identify the Solids in Practice
- From the Diagram to the Structure
We draw Metatron’s Cube from memory, tracing thirteen circles in a web that looks like a blueprint for something larger than itself. The compass point pierces the paper, and the eye follows lines that form triangles, squares, pentagons. The hand knows before the mind does: these are the Platonic solids, nested inside the geometry of the archangel.
Metatron’s Cube is a two-dimensional diagram of thirteen equal circles connected by straight lines, containing all five Platonic solids (tetrahedron, cube, octahedron, dodecahedron, icosahedron) in their nested relationships. The cube is not a cube. It is a map of the scaffolding beneath visible reality.
What Are the Platonic Solids, Exactly?
Plato named them in the Timaeus (circa 360 BCE), assigning each to one of the classical elements. The tetrahedron (four triangular faces) was fire. The cube (six square faces) was earth. The octahedron (eight triangular faces) was air. The icosahedron (twenty triangular faces) was water. The dodecahedron (twelve pentagonal faces) was the shape of the cosmos itself.
But Plato did not invent them. The Pythagoreans had studied these forms a century earlier, and neolithic peoples carved stone spheres approximating regular polyhedra as early as 2000 BCE in Scotland. What Plato did was connect geometry to metaphysics: if the universe had a rational structure, these five shapes were its vocabulary.
The mathematician Euclid proved in his Elements (circa 300 BCE) that only five regular convex polyhedra exist. The proof is elegant and final. No sixth shape can satisfy the conditions: identical faces, identical vertices, all edges equal. These five are complete. They are the only game geometry allows.
Where Metatron’s Cube Comes From
The diagram appears first in Jewish mystical texts. The Sefer Yetzirah (Book of Formation, compiled between the 2nd and 6th centuries CE) describes the “thirty-two paths of wisdom”: ten sefirot (emanations of God) plus twenty-two letters of the Hebrew alphabet. Some later Kabbalists visualized these paths as a geometric network.
Metatron himself is the highest of angels in Merkabah mysticism, the celestial scribe who sits “near the throne of glory.” The Third Book of Enoch (circa 5th-6th century CE) describes him as transformed from the patriarch Enoch into an angel of fire with thirty-six wings. His cube is the pattern of creation that he guards.
The specific diagram we call Metatron’s Cube emerges in medieval Kabbalistic texts. The earliest known visual representation appears in a 13th-century manuscript of the Sefer Raziel HaMalakh, though the scholar Aryeh Kaplan noted that the geometric principles were encoded in earlier Jewish meditation manuals. By the Renaissance, Christian Hermeticists like John Dee (1527-1608) were incorporating the pattern into their own angelic magic systems, blending Kabbalah with Neoplatonic geometry.
How the Five Solids Fit Inside the Thirteen Circles
Draw thirteen circles in a hexagonal flower pattern. Connect the centers of every circle to every other circle with straight lines. The resulting network contains the five Platonic solids, each one defined by a subset of the lines.
The cube is the most visible. Look at the six circles that form a hexagon around the center. Connect their centers. Now connect those to the center circle. You have the corners of a cube folded flat. The cube’s eight vertices correspond to eight of the thirteen centers.
The tetrahedron appears when you connect four non-adjacent circle centers. It is the simplest solid and the easiest to miss. Its four triangular faces map onto the diagram as a star tetrahedron (two tetrahedra interpenetrating), which some call the Merkabah itself.
The octahedron is the dual of the cube. Where the cube has eight vertices, the octahedron has eight faces. In Metatron’s Cube, the octahedron’s six vertices sit at the centers of the six outer circles of the hexagon. Its edges are the lines connecting those circles to the center.
The icosahedron and dodecahedron are harder to see. They require extending the lines of Metatron’s Cube into three dimensions. The icosahedron’s twenty triangular faces and the dodecahedron’s twelve pentagonal faces emerge from the golden ratio relationships embedded in the cube’s geometry. The 19th-century geometer H.S.M. Coxeter demonstrated that these two solids are duals of each other, each containing the other’s vertices in its face centers.
The result is a single diagram that encodes all five. No other two-dimensional pattern does this.
Why This Relationship Mattered to the Kabbalists
The medieval Kabbalists saw Metatron’s Cube as a meditation device, not a puzzle. The thirteen circles represented the thirteen attributes of divine mercy described in Exodus 34:6-7. To trace the lines was to move through the sefirot, each solid corresponding to a different level of creation.
The tetrahedron corresponded to Atzilut (the world of emanation), the purest level where nothing is separate from the divine. The cube corresponded to Assiyah (the world of action), the material plane where we live. The remaining solids mapped to Beriah (creation) and Yetzirah (formation). The dodecahedron, with its twelve pentagonal faces, represented the outermost sphere of the fixed stars, the boundary between the created universe and the unknowable Ein Sof (the infinite).
When the Kabbalist meditated on Metatron’s Cube, they were not looking at a symbol. They were traversing the structure of existence, moving from the material cube at the bottom to the cosmic dodecahedron at the top. The solids were not abstract. They were stations on a journey.
What the Renaissance Magicians Did With It
John Dee kept a wax seal engraved with Metatron’s Cube. He used it in scrying operations with Edward Kelley, placing it on a table beneath the “shew-stone” (a polished obsidian sphere). Dee believed the cube was a key to angelic language: the Enochian system he and Kelley received in the 1580s contained geometric patterns that echoed Metatron’s Cube.
The Renaissance Hermeticist Heinrich Cornelius Agrippa (1486-1535) published similar diagrams in his De Occulta Philosophia. He connected the solids to planetary magic. The cube belonged to Saturn. The tetrahedron to fire elementals. The icosahedron to water spirits. The diagram was a summoning grid, a way to align the magician’s space with the geometric order of the heavens.
This tradition survived into modern ceremonial magic. The Hermetic Order of the Golden Dawn (founded 1888) used Metatron’s Cube as a basis for temple layouts and talismanic designs. Aleister Crowley included it in his 777 tables. The Theosophical Society popularized it further in the early 20th century, stripping away the angelic names and presenting it as “sacred geometry” accessible to anyone with a compass and straightedge.
The Mathematical Objectivity Behind the Symbolism
Mathematics confirms what the mystics intuited. The five Platonic solids are the only possible regular polyhedra because the sum of angles at any vertex must be less than 360 degrees. This is not belief. It is proof.
Metatron’s Cube contains them because the thirteen circles in hexagonal arrangement define a set of points that correspond to the vertices of the cube octahedron (a quasi-regular solid with eight triangular faces and six square faces). The cube octahedron in turn contains the Platonic solids as subsets of its vertices and as duals of those subsets.
The ratio of the distance between two adjacent circle centers to the distance between opposite circle centers in Metatron’s Cube is √3, the same ratio that appears in the diagonal of a cube. The golden ratio φ (approximately 1.618) appears in the relationship between the cube and the dodecahedron. The numbers are not symbolic. They are the actual numerical values embedded in the drawing.
What People Get Wrong About This Diagram
The most common error is thinking Metatron’s Cube and the Flower of Life are the same pattern. They are not. The Flower of Life is a simpler design of nineteen overlapping circles with no connecting lines between centers. Metatron’s Cube always includes straight lines connecting every circle center to every other center. The Flower of Life is the seed; Metatron’s Cube is the structure that grows from it.
A second misunderstanding: that the cube itself appears as a visible cube in the diagram. It does not. The cube is implied by the relationships between vertices. Beginners often search for a six-faced box in the lines and miss the cube entirely because they expect it to look like a die.
Third: that Metatron’s Cube is a Christian symbol. It originates in Jewish Kabbalah. Christians adopted it later, but its angel is Metatron, a figure who has no direct equivalent in Christian angelology. The Protestant reformers of the 16th century would have considered its use idolatrous.
Finally, some claim the diagram appears in ancient Egyptian temples. We have found no evidence for this. The earliest verified examples date to medieval Europe. Claims of predynastic or Atlantis origins belong to 19th-century Theosophical speculation, not to documented history.
How to Identify the Solids in Practice
Take a clear drawing of Metatron’s Cube. Find the central circle. Mark it. Now find the six circles that surround it in a perfect hexagon. The lines between these six circles and the central circle define the vertices of a cube. Rotate the drawing and you will see the cube’s faces mapped as rhombuses, not squares, because the diagram is a two-dimensional projection of a three-dimensional form.
To find the tetrahedron, look for four points that are equidistant from each other. In Metatron’s Cube, every group of four non-adjacent circle centers forms a tetrahedron. There are multiple tetrahedra overlapping. That is why some call it the “star tetrahedron” or Merkabah.
The octahedron appears as the intersection of two such tetrahedra. Its six points are the six outer circles of the hexagon. Its eight faces are the eight triangles formed by connecting these six points in alternating sets.
The dodecahedron and icosahedron require you to imagine the cube extended into the third dimension. If you take the cube’s eight vertices and add six more at the centers of its faces, you have the fourteen vertices of the cube octahedron. From this structure, the dodecahedron and icosahedron can be derived by truncating vertices or faces. The lines of Metatron’s Cube encode these operations.
FAQ
Is Metatron’s Cube in the Bible? No. The name Metatron appears in extra-biblical Jewish texts like the Third Book of Enoch (5th-6th century CE), but the cube diagram itself is a medieval Kabbalistic development.
Can you draw all five Platonic solids from Metatron’s Cube? Yes, but the dodecahedron and icosahedron require extending the two-dimensional diagram into three-dimensional space. The cube, tetrahedron, and octahedron are directly visible.
Does Metatron’s Cube have anything to do with the golden ratio? Yes. The relationship between the cube and the dodecahedron within the cube involves the golden ratio φ (1.618), which governs the pentagonal symmetry of the dodecahedron.
Why thirteen circles? The number corresponds to the thirteen attributes of divine mercy in Jewish tradition (Exodus 34:6-7) and to the thirteen sefirot when including the Da’at (knowledge) as a hidden sefirah. The practical geometric reason is that thirteen circles in hexagonal packing produce the maximum symmetry for the cube octahedron.
From the Diagram to the Structure
The cube is not the point. The diagram is not the point. The point is what happens when you realize that the same geometry that governs a snowflake also governs a Kabbalist’s meditation chamber. The five solids inside Metatron’s Cube are not secrets. They are demonstrations. Geometry proves what mysticism asserts: that the same pattern repeats from the microscopic to the cosmic, and that a circle drawn in sand participates in the same mathematics as the orbit of a planet.
For a deeper look at how the Platonic solids relate to the classical elements, see our guide to sacred geometry and the elements. To understand how Metatron’s Cube connects to other Kabbalistic diagrams, visit the sacred geometry hub. And for the relationship between these solids and the Flower of Life pattern, read our article on the Flower of Life and the seed of creation.