Up to now, we have been mainly concerned with plane figures like triangles, recatangles, pentagons and hexagons that were seen to be component parts of the Tree of Life and Metatron's Cube; we will now turn our attention to solid figures. As it turns out, not only are the Star of David and Tree of Life contained within the figure of Metatron's Cube, but so are all the Platonic Solids.
Plato's name is forever connected with solid geometry and its place in the workings of our universe. 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.
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.
The 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 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; 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."
Look closely at the dodecahedron (below left), with it's 12 pentagonal faces, and Metatron's Cube (below right), composed of thirteen circles. Note that each circle but one in the cube figure is associated with a face of the dodecahedron; and that one, the central circle (one surrounded by 12), is located where three of the faces come together.
The nine blue circles are associated with the centers of nine of the faces of the dodecahedron, six of which we can see, while three (the ones at the corners of the red triangle in Metatoron's Cube) are angled away from us. [Note that extending the hexagons in the Cube, gives us the location of the corners of the pentagons.] The three red circles located at the end of the line segments that form the "Y" around the center, correspond to the centers of the three faces on the "back side" of the dodecahedron.
We can see, then, that instead of the dodecahedron being "generated" by Metatron's Cube, the cube "maps onto" the dodecahedron, confirming what Plato said about God embroidring figures on it. We can see, as well, that the A-shaped Tree also maps to the dodecahedron, thereby showing the logic for using a tree-form with an explicit pentagon in it.
After having shown the Tree of Life in both the cathedral plan and the DC plan, and the Tree mapping to Metaron's Cube and the Dodecahedron, we now show how the Cube relates to the DC map. [BTW - if you got here from page 5, one click back should take you to the image of the Tree in the DC and cathedral plans.]
Looking first at the image on the left, we see that the White House occupies the central circle of the Sun, the corner of the dodecahedron where three of the pentagonal faces meet; while Scott Circle (white), the National Archives Building and the Navy Medical and Surgical Center (both in blue) each occupy the center one of the three middle pentagonal faces outlined in red. The Jefferson Memorial (green) and the Capiotol (blue) both occupy the centers of faces, as does the point of the triangle in the map (which can't be seen on this image of the Cube). That's six of the twelve faces.
Turning to the image on the right, we see the other three corners of the big rectangle higlighted in blue; just as with the Capitol, these others also fall on a center of a dodecahedron face; making nine. Note that one of these is centered on Georgetown, and that Pennsylvania Avenue marks the diagonal of this rectangle.
Remember that 3 faces of the dodecahedron are completely hidden; these are represented by the Washington Monument (blue), Washington Circle and Mt Vernon Square (both red), all of which are at the ends on the line segments that form the "Y" centered on the White House, and all of wehich are associated with George Washington. These as well as DuPont Circle and Logan Circle (both in red near the peak of the triangle in the map, all fall on corners where pentagonal faces meet.
I have included an image map of the Cube/Tree of Life super-imposed onto the DC map, showing how the spheres of the Tree correlate to DC landmarks, which illustrates my thesis about the Tree being used as a template for the map. [Note that the National Archive Building located at the position of the seventh sphere is numbered 700 Pennsylvania Avenue.]
