Hexagrams and hexagons are metaphysical archetypes. It’s fun watching them form if you have a compass and straightedge. Turn a circle, and then with the same opening walk the compass around the circle to form six points. Make an upward pointing male triangle and a downward pointing female one.
The hexagram’s symbolism is rich. Here Earth and Heaven meet with you in the center. You are surrounded by the six directions, or the six days of creation with you the perfectly still axis of the Sabbath where you find refuge from the constantly changing world of form, reminding us a little of 中.
Make our hexagram a hexagon. When each side of the six has the value 1, then the distance from one side to another on the opposite side equals 1.732…, the square root of three, also the key relationship of the vesica piscis and the cube.
Now three dimensionalize our hexagram. We now have a lovely star tetrahedron. Geometry manifests what is implicit and there is a lot here to bring out. The star tetrahedron fuses with a cube and inside that cube is an octahedron. A dodecahedron contains the star tetrahedron and an icosahedron contains the dodecahedron. See my photo from a February 20th 2009 entry to get a better idea. Better yet, get Robert Lawlor’s Sacred Geometry (see my links) and make the diagram yourself.
Six is a perfect number because it is the sum of its divisors, 1, 2, 3. Factorial 6, or 6! is 720. The sums of the angles of a hexagon and the tetrahedron are 720. The four other Platonic Solids are based on this special number. 720 is also the magic number used to three dimensionalize the Cosmological Circle diagram (see Michael Schneider’s book for that in my links). Those same numbers happen to be those that define our place in the cosmos, such as 2,160, one Platonic Month (1/12 of a Platonic Year, 25,920 years, the long shifting of the ages, the result of the Earth’s slight axial wobble).
For much more on hexagrams and all things geometric, check out my links.
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