From the Hexagon to the Pentagon

We have so far investigated a flat, two dimensional imagery of the surface of the earth, but of course, the earth is a sphere and as such the geometrical pattern must evolve to accommodate its curved surface. The following quote from the « Phaedo » by Plato, provides us with a vital clue to the next stage of its evolution.

« But if I must tell you a story, Simmias, it is worth hearing what things really are like on the

earth under the heavens... It is said then, my comrade, that first of all the earth itself looks from above, if you could see it, like those twelve patch leather balls »

A sphere, equally divided into twelve parts, results in twelve, equal, five-sided « curved » pentagons. Plato also tells us in the « Timaeus » of the five, equal-sided, equal-angled polyhedra, known as the Platonic solids, which he considered to be the basic building blocks of all matter. These « regular solids », the tetrahedron (4 sided), cube (6 sided), octahedron (8 sided), dodecahedron (12 sided) and the icosahedron (20 sided), are all developed from the right-angled isosceles triangle and the half equilateral triangle, the two triangles that we associated with the start of the geometrical pattern of consciousness.

The geometrical curiosity of these five, regular polyhedra, is that they can be perfectly fitted within each other, whereby the twelve icosahedron corners fit precisely into the centres of the twelve faces of the dodecahedron, and the twenty corners of the dodecahedron fit perfectly into the centres of the twenty faces of the icosahedron. The intersection of the edges of these two figures indicates the corners of the octahedron. The corners of the tetrahedron and cube also fall precisely into the corners of the dodecahedron. Of profound importance, is that the five polyhedra are perfectly inscribable within a sphere. That is, if a sphere were made to contain tightly any one of the five figures, all of the figure’s corners would precisely touch the sphere’s surface.

With regards to the sphere of the earth, we find that an internal dodecahedron would project its twelve, pentagonal faces onto its curved surface. Similarly, an external dodecahedron which contains exactly the sphere of the earth would project its faces to exactly the same positions.

The geometrical development of the divine pattern can now be continued to determine its conformity with an external dodecahedron which could exactly contain the known diameter of the earth. The flat pentagons can then be projected onto the earth’s surface to see how they coincide with its natural features.

The Positional Importance of Chartres

The distance between Orleans and Brioude is 2/phi x 2⁸ Km and between the two points of the French zodiac at Rouen and Nimes, 2/phi x 2⁹ Km. The next step in this progression is 2/phi x 2⁸ x 3 Km (Fig 23), which gives a seal of Solomon with one point in the English Channel and the other in the Gulf of Lions. The actual distance between points is 949,32 Km. Chartres marks the position of the cross formed by the central Cancer/Capricorn axis and the lower equilateral triangle of the seal of Solomon. These two equilateral triangles fit precisely into an enclosing pentagon, which is crucial in the development of one face of the dodecahedron.

Chartres cathedral, therefore, indicates an important transition from the seal of Solomon to the pentagon. The geometrical relationship between them gives us the unit of measurement used

for the dimensions of the cathedral’s internal area, or the space enclosed by the cathedral.