Metatron's Cube

Definition

Pronunciation: meh-TAH-tronz KYOOB

Also spelled: Metatron Cube, Fruit of Life Matrix

A two-dimensional figure derived from connecting the centers of thirteen equal circles (the Fruit of Life configuration) with straight lines. The resulting 78-line pattern contains two-dimensional projections of all five Platonic solids and serves as a map of the fundamental forms of three-dimensional space.

Etymology

Named for Metatron, the archangel of Jewish and Christian esoteric tradition who serves as the celestial scribe and mediator between divine and human realms. The name Metatron itself has disputed origins: possibly from the Greek meta thronon (beyond the throne), the Latin metator (measurer), or a corruption of Mithras or Matatron. The association of the geometric figure with Metatron emerged in twentieth-century sacred geometry literature, drawing on Kabbalistic traditions that describe Metatron as the guardian of the Tree of Life and the keeper of divine geometry.

About Metatron's Cube

The construction of Metatron's Cube begins where the Flower of Life leaves off. From the Flower of Life's overlapping circles, a specific subset of thirteen circles is extracted — the Fruit of Life — arranged with one circle at the center and twelve surrounding it in two concentric rings (six in the inner ring, six in the outer ring, rotated thirty degrees from the inner). When every center point is connected to every other center point by a straight line, the result is 78 lines (the combination formula 13-choose-2) forming a figure of extraordinary density and symmetry. This is Metatron's Cube.

The figure's significance in sacred geometry rests on a demonstrable geometric property: within its line network, all five Platonic solids can be identified as subsets of connected vertices. The tetrahedron appears as four points connected by six lines. The cube (hexahedron) appears as eight points connected by twelve edges. The octahedron's six vertices and twelve edges are traceable within the pattern. The dodecahedron's twenty vertices and thirty edges can be located through a specific three-dimensional projection. The icosahedron's twelve vertices and thirty edges complete the set. Plato argued in the Timaeus (c. 360 BCE) that these five solids constitute the geometric atoms of the physical world — earth (cube), water (icosahedron), air (octahedron), fire (tetrahedron), and cosmos (dodecahedron). Metatron's Cube, by containing all five, functions as a geometric map of Plato's entire elemental system.

The Kabbalistic dimension of the figure connects to the Sefer Yetzirah (Book of Formation, composed between the 2nd and 6th century CE), which describes creation as occurring through the combination of the twenty-two Hebrew letters and the ten Sephiroth. The thirteen circles of Metatron's Cube have been mapped by contemporary researchers onto the ten Sephiroth plus the three hidden or implied aspects (Da'at and the two aspects of Keter). This mapping is not universally accepted within Kabbalistic scholarship, but it demonstrates the structural compatibility between the geometric and mystical systems.

The archangel Metatron occupies a unique position in Jewish angelology. The Talmud (Bavli, Hagigah 15a) describes Metatron as the only angel permitted to sit in the divine presence — a privilege that led the sage Aher (Elisha ben Abuyah) to heretically conclude there were 'two powers in heaven.' The Third Book of Enoch (Sefer Hekhalot, 5th-6th century CE) identifies Metatron with the transformed patriarch Enoch, who was taken into heaven and transfigured into an angelic being with seventy-two names and a body of fire. Metatron is described as the measurer of heaven, the scribe who records all actions, and the guardian of the threshold between the human and divine worlds. The geometric figure bearing his name functions analogously — it is the threshold pattern through which the formless (the point, the circle) becomes the formed (the five regular polyhedra, the building blocks of three-dimensional space).

Euclid devoted the final and culminating book of the Elements — Book XIII — to the construction of the five regular solids and the proof that no others exist. His proof of completeness (there are exactly five convex regular polyhedra, no more) remains one of the most elegant results in mathematics. The significance for sacred geometry is that five — not four, not six, not infinitely many — represents the complete set of possible perfect forms in three-dimensional space. Metatron's Cube encodes this completeness in a two-dimensional figure, making visible the finite vocabulary of spatial perfection.

Kepler revived Plato's geometric cosmology in the Mysterium Cosmographicum (1596) by nesting the five Platonic solids inside each other, separated by the orbits of the six known planets. The ratios between the solids' inscribed and circumscribed spheres, Kepler argued, determined the relative distances of the planets from the sun. Although this model was eventually superseded by Kepler's own discovery of elliptical orbits, it demonstrates the persistent conviction — from Plato through the Renaissance — that the Platonic solids, and therefore the structure encoded in Metatron's Cube, represent the fundamental architecture of physical reality.

In contemporary sacred geometry practice, Metatron's Cube is used as a meditation object. Practitioners trace the lines connecting the thirteen circles, visualizing the emergence of each Platonic solid in three dimensions. The practice is described as a method of training spatial intuition — the ability to see three-dimensional forms embedded in two-dimensional patterns — and as a contemplative exercise in recognizing how complexity (five distinct solid forms with different symmetries, face counts, and vertex configurations) can emerge from simplicity (thirteen equal circles, all points connected).

The mathematical properties of the figure extend into group theory and symmetry analysis. The complete graph K13 (all thirteen points mutually connected) has the symmetry group S13, which contains over six billion elements. The Platonic solids embedded within it are subgroups with their own distinct symmetry operations — rotations and reflections that leave each solid unchanged. The relationship between the full symmetry of Metatron's Cube and the restricted symmetries of its embedded solids parallels the Kabbalistic concept of tzimtzum — the divine contraction through which the infinite (Ein Sof) limits itself to produce the finite forms of creation.

R. Buckminster Fuller explored the geometric properties of this figure through his concept of the vector equilibrium (cuboctahedron) — a shape with twelve vertices arranged around a center point, which he considered the ground state of spatial geometry. Fuller's Synergetics (1975, 1979) argued that nature's coordinate system is not the Cartesian grid (cubes) but the isotropic vector matrix — an arrangement of points corresponding to the centers of closest-packed spheres, which generates Metatron's Cube when fully connected. Fuller's work demonstrated that the figure is not a medieval curiosity but an expression of the geometric principles governing crystal formation, molecular bonding, and structural engineering.

Significance

Metatron's Cube occupies the critical junction between the two-dimensional world of circle patterns and the three-dimensional world of solid forms. It is the geometric moment where the Flower of Life's planar beauty becomes the Platonic solids' spatial architecture. This transitional function — mediating between dimensions — mirrors the role of the archangel Metatron in Jewish mysticism: the mediator between the formless divine and the formed creation.

The figure's demonstration that five and only five regular convex polyhedra exist encodes a profound mathematical truth: the possibilities for perfect spatial form are finite. Three-dimensional space permits exactly five kinds of regularity, and all five are contained in one two-dimensional drawing. This containment of three-dimensional completeness within a two-dimensional pattern is geometrically remarkable and philosophically provocative — it suggests that higher-dimensional truths are always already present in lower-dimensional structures, awaiting recognition.

For practitioners of sacred geometry, Metatron's Cube serves as proof of concept that simple operations (draw circles, connect centers) produce the complete vocabulary of spatial form. The entire material world, in the Platonic reading, is built from these five shapes — and all five emerge from thirteen circles on a flat surface.

Connections

Metatron's Cube is derived from the Flower of Life through the intermediate Fruit of Life pattern, and it contains all five Platonic solids as embedded subsets. The Seed of Life (seven circles) is the first stage of the construction that eventually yields the thirteen-circle framework.

The figure's Kabbalistic associations connect it to the Tree of Life — both systems map the process by which unity differentiates into multiplicity. In the Hermetic tradition, Metatron's Cube illustrates the axiom 'as above, so below' — the three-dimensional solids are contained within the two-dimensional figure, just as the material world is contained within the ideal.

Buckminster Fuller's vector equilibrium relates the figure to the torus — the cuboctahedron at the Cube's center represents the point of maximum equilibrium from which toroidal energy flow radiates outward and returns.

See Also

• Flower of Life
• Merkaba
• Platonic Solids
• Seed of Life
• Vesica Piscis

Further Reading