Framework

The basic unit in Synergetics is the Tetrahedron. It is composed of four vertices and six edges. It is outlined in yellow in the above diagram.

If you include an imaginary point in the center, there are five points. And there are five element: Fire, Water, Air, Earth, and Spirit.

Bisecting each edge yields six new point. Connecting them creates an Octahedron, outlined in blue above.

If you include an imaginary point in the center, there are seven points. And there are seven planets. (Uranus, Neptune, and Pluto will be dealt with later)

Bisecting each edge of the Octahedron yields twelve new points. Connecting them creates a Cuboctahedron or Vector Equibrium, outlined in red above. This is the only regular geometric solid where the distance between any two vertices is the same distance as between a vertex and the center.

There are twelve points, thirteen with the center point. There are twelve signs of the zodiac. The problem of the "thirteenth sign" of the zodiac will be dealt with later.

The main problem is assigning the planets and zodiac signs to the appropriate sphere. Refer to the following diagram:

The diagram is a humorous one from a blog called Indexed. But it reveals a methodology. For example, given that the sins at either end of line BG are "Gluttony" and "Pride", that line will have to somehow combine the two sins. The author figures this is best represented by "Fat men in Speedos."

On the framework, the elements are the vertices of the tetrahedron. The blue points are midway between the vertices, in other words, they are like the line segments in the "seven deadly sin" diagram.

So the blue point between the element Fire and the element Air would the planet closest to being a combination of Fire and Air. My personal view was since the elemental weapon of Air is a sword, and Fire symbolizes energy, an energetic sword was more or less War, and thus would correspond to the planet Mars, god of War.

There is a vaguely similar methodology associated with the Qabalistic diagram "The Tree of Life." The spheres are called "Sephiroth", the lines connecting them are called "Paths". The various Tarot cards can be attributed to various Sephiroth and Paths. The number cards correspond to Sephiroth and the Trumps correspond to Paths.

So much in the same way that the "Glutton-Pride" line is "Fat men in Speedos," the Tiphareth-Chesed path is "The Hermit". The difference is that the seven deadly sins use logical reasoning and the Tarot uses Qabalistic intuitional thought.