Enoch, The Kabbalah, and the Glass Bead Game
Metatron's Cube is usually presented as 13 circles and the lines that connect the centers of those. The first things that you see are triangles, hexagrams, hexagons and a rectangle. The cube is easier to see if we add six more circle bringing the total to 19; it then becomes apparent that the figure with thirteen circles is an abbreviation for a 3 x 3 x 3 cube (3 cubed) composed of 27 cirlces.
As you can see 8 circles (2 cubed) are hidden in the 3 cube, just as 1 circle (1 cubed) is hidden in the 2 cube. The 4 cube conceals the 3 cube etc.
Overlapping the circles in Metatron's Cube shows that the cube is equivalent to the Flower of Life comprised of vesicas. One version of the Tree of Life (Kircher) derives from the flower image. Note how the hexagon still rules this figure.
Metatron's cube is connected numerically to the 3 x 3 Square of Saturn. While the volume of the cube is 27, the surface area is 6 x 9 or 54, twice the volume. In the 6 x 6 x 6 cube (connected to the sun), the surface area and the volume are the same number.
In the 9 x 9 x 9 cube (connected to the moon) the volume is 729 while the surface area is 486 (729 = 1.5 x 486). 729 is the number equivalent of Cephas (Aramaic for rock), the name given to Simon Peter ("You are Simon, the son of John. You will be called Cephas."), while 486 is the equivalent of rock (Greek petra), as in 'Thou art Peter, and upon this rock I will build my church'.
729 is the smallest odd number greater than 1 that is both a cubic number and a square number (9 cubed and 27 squared). The smallest even number (greater than one) that works is 64 (4 cubed and 8 squared like the checker board).
The 27 by 27 magic square (above right) has been dubbed the Calendar Square, because it has the number 365 at the center (Enoch lived 365 years), and because 729 is said to represent 365 days and 364 nights. The Sum of the whole 27x27 square is 9,855 being the number of days in a 27 year period. The Sum of the inner and central 3x3 square is 1,095 being the number of days in a 3 year period. The Sum of the central 9x9 square is 3,285 being the number of days in a 9 year period. Note that there are nine 9x9 squares in the figure.
The image below shows Plato contemplating a cube in a courtyard. The cube is the 9x9x9 cube while the courtyard is 27x27, where the surface area of one is the volume of the other. The 4x4x4 cube occupies the center of the 8x8 square (the checkerboard) in the same manner.
The Platonic solids (described by Plato in his Timaeus ca. 350 BC) are all of the three-dimensional solids that you can define using faces that are identical regular polygons. (that is plane solids with equal length sides like the triangle, square and pentagon). There are five of these: the Tetrahedron (4 triangular faces and 4 corners), the Cube (6 square faces and 8 corners), Octahedron (8 triangular faces and six corners- a double pyramid), Icosahedron (20 triangular faces and 12 corners) and Dodecahedron (12 pentagonal faces and 20 corners). Each of these figures nests in a sphere so that all it's corner's are touching the circumference.
The solids are also known as the three-dimensional regular polytopes, and have been known since Neolithic times. This animation shows all the platonic solids formed within Metatron's Cube. Note how the faces triangulate.
These solid figures were used by the Platonists to symbolise the four elements - Fire by the Tetrahedron, Air the Octahedron, Water the Icosahedron, and Earth the Cube, and the sphere of the Universe, the stuff of which the constellations and heavens were made, by the Dodecahedron.
Plato's Timaeus is a essay on virtually every aspect of physical existence expressed in terms of these four basic elements and their transmutations and re-assembled forms. While the details of Plato's cosmology, or account of the universe are not very satisfactory from the modern point of view, we can see obvious counterparts in the modern theory of chemistry.
Plato (427-347 BC) carefully lays out his reasoning for ascribing certain geometric shapes to each of the four elements of matter. As the lightest and sharpest of the elements, fire was a tetrahedron. As the most stable, earth consisted of cubes. Water was an icosahedron, and air was an octahedron. The universe itself was a perfect sphere.
The fifth regular solid, the dodecahedron, identified with the quintessence, is barely mentioned. Plato merely notes that "there is still one construction left, the fifth, God made use of it for the universe when he painted it." Another translation reads "God used this solid for the whole universe, embriodering figures on it". There was a Pythagorean notion that the dodecahedron formed the"timbers" on which the spherical bulk of the heavens was built. Indeed, the structure of the world was sometimes compared to that of building a ship, where the keel and ribs would be laid out first.
Curiously, in the earlier Phaedo, Plato described the earth itself, when viewed from above, as "many-colored like the balls that are made of twelve pieces of leather." Note that the dodecahedron is the solid which most closely approximates the sphere.
In the first image below, we can see that Metatron's Cube maps to a stellated dodecahedron. The thirteen circles of the cube figure correlate to the front corner and the twelve 'faces' of the dodecahedron (12 around 1). Note that that means that three of the circles match faces on the 'back side' of the figure. The Tree of Life maps to the dodecahedron using the middle of the faces and the corners where the faces meet. The top point of the blue hexagon, the center of the top pentagram is Daath, and is not marked on the tree.
If the cube represents matter, materiality and the world, this image can be said to show that the dodecahedron provides a kind of framework for the cube, as is suggested above. Notice that this image creates the illusion that the cube results from stellating a dodecahedron, and that the dodecahedron results from removing corners of the cube.
I'm going to call this figure Enoch's Cube which contains the hexagon that doubles as a cube, the equilateral triangle/tetrahedron, the star of david (hexagram - two triangles), metatron's cube, the tree of life and the dodecahedron. It also provides the isometric grid pattern that you need to do perspective drawing.
Masons use the term 'rough ashlar' to refer to a free stone that has been seperated from it's source, and the term 'perfect ashlar' to refer to the finished stone. The rough stone is the raw material (called the first matter by alchemists) and the perfect ashlar is the finished product. This first matter is represented by the Shekinah as the stone that fell from heaven and by figures like Jesus, said to be the 'first born' of creation, the only begotten son of God. The finished stone is represented by the completed world.
Philosophically these are the macrocosm and the microcosm, represented by the hexagon and the pentagon; in the figure above they are represented by the cube (concealed within the hexagon) and the dodecahedron (composed of 12 pentagonal faces). The same ideas are illustrated by this MC Escher print.