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Geometry and creation.
         The role of geometry in the process of creation is covered well by Robert Lawlor, in his fascinating book Sacred Geometry: Philosophy and Practice (Thames and Hudson, London, 1982). In it he says the following: "The perspective of volume offers yet another metaphor for the original and ever-continuing creative act of the materialization of Spirit and the creation of form. The very ancient creation myth coming from Heliopolis in Egypt gives an example of this mode of envisioning. Nun, the Cosmic Ocean, represents pure, undifferentiated spirit-space, without limit or form. It is prior to any extensive, any specificity, any god. It is pure potentiality. By the seed or will of the Creator, who is implicit within this Nun, the undifferentiated space is impelled to contract or coagulate itself into volume. Thus Atum, the creator, first creates himself or distinguishes himself from the undefinable Nun by volumizing, in order that creation might begin."
The Five Platonic Solids.
        "What form, then, might this first volume have? What indeed are the most essential volumetric forms? There are five volumes which are thought to be the most essential because they are the only volumes which have all edges and all interior angles equal. They are the tetrahedron, octahedron, cube, dodecahedron and the icosahedron, and are the expressions in volume of the triangle, the square and the Pentagon: 3, 4, 5. All other regular volumes are only truncations of these five. These five solids are given the name 'Platonic' because it is assumed that Plato has these forms in mind in the Timaeus, the dialogue in which he outlines a cosmology through the metaphor of planar and solid geometry."

        In this dialogue, which is one of the most thoroughly 'Pythagorean' of Platos works, he establishes that the five elements of the world are earth, air, fire, water and aether (prana). Lawlor continues: "Plato's fabricator of the universe created order from the primordial chaos of these elements by means of the essential forms and numbers. The ordering according to number and form on a higher plane resulted in the intended disposition of the five elements in the physical universe. The essential forms and numbers then act as the interface between the higher and lower realms. They have in themselves, and through their analogues with the elements, the power to shape the material world.
         "As Gordon Plummer notes in his book The Mathematics of the Cosmic Mind, the Hindu tradition associates the icosahedron with the Purusha. Purusha is the seed image of Brahma, the supreme creator himself, and as such this image is the map or plan of the universe. The Purusha is analogous to the Cosmic Man, the Anthropocosm of the western esoteric tradition. The icosahedron is the obvious choice for this first form, since all the other volumes arise naturally out of it."

The star born within the pentagon:

Patterns created from the moving 3-D Icosahedron lattice above:
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The Golden Ratio.
        The golden ratio is the mathematical proportion 1:1.618034...ad infinitum. Often called by its Greek name phi, it is also known as the Divine Proportion, the Golden Ratio, the Golden Section and the Golden Mean. It is indelibly inscribed in the heart of nature and man. Trace the thread of this "golden mean" from daisy to pyramid, from pine cone to Parthenon. Or from seashell to spiral nebulae as described above. The cosmos weaves its garments with perfect integrity, laced by the golden ratio. It is so omnipresent that many philosophers, artists, mathematicians, and scientists have considered it an essential component of beauty, perhaps integral to life itself. Plato considered it the key to the physics of cosmos. The Egyptians thought it more than a number and believed it symbolized the creative process and the fire of life.
        This magical proportion is found by dividing a line (AC) at a particular point to yield two unequal sections, where the smaller one (AB) is proportionate to the larger one (BC) as the larger one (BC) is to the entire line (AC). The ratio is expressed as AB/BC = BC/AC. There is only one such point (B) on any line. It is easy to produce this ratio geometrically. One of many ways is the five-pointed star, as drawn within a pentagon above. Every outside line on the pentagon is in a phi ratio to any line of the star. Also, every line on the star has 3 segments. One side segment is in a ratio of 1:1.618 to the rest of that line. This ratio is what was used in the architecture of the great pyramids of Egypt, and results in the focusing of universal energy (a.k.a. prana) at a particular point, which helps in rejuvenation of life (or the preservation of dead bodies). This resurrection energy and ratio is the mark of the Christ, the victor over death and rejuvenating principle in nature.
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Phi and the Great Pyramid.

         In the diagram above, the big triangle is the same proportion and angle of the Great Pyramid, with its base angles at 51 degrees 51 minutes. If you bisect this triangle and assign a value of 1 to each base, then the hypotenuse (the side opposite the right angle) equals phi (1.618..) and the perpendicular side equals the square root of phi. And that’s not all. A circle is drawn with it’s centre and diameter the same as the base of the large triangle. This represents the circumference of the earth. A square is then drawn to touch the outside of the earth circle. A second circle is then drawn around the first one, with its circumference equal to the perimeter of the square. (The squaring of the circle.) This new circle will actually pass exactly through the apex of the pyramid. And now the “wow”: A circle drawn with its centre at the apex of the pyramid and its radius just long enough to touch the earth circle, will have the circumference of the moon! Neat, huh! And the small triangle formed by the moon and the earth square will be a perfect 345 triangle (related to the Pythagorean Theorem). Using the 345 triangle is also the easiest way to draw a squared circle.