A Polygram, or Complete Graph, is a construct in which every point has a line drawn to every other point. In terms of Mathematics and Geometry, it is a simple curiosity, however in terms of magic it is far more potent, as each point can represent an Element, and so the lines and geometric shapes hold great power.
Powers of the Polygrams Edit
There are three very important Polygrams nessecary for most mages to learn: The Pentragram, Octogram, and as of the events of the First Game, the Nonagram. These are important as many sources of magic work well in fives, the Base Elements, for a long time were believed to be Eight, and the Nonagram holds the great and powerful Ninth Element. Despite this fact, each has power on its own accord, detailed below.
A single point, useful for monocoloured magics.
Duograms hold their importance as sybolising Lines of Power, important in Magic Theory.
Trigrams are simple triangles, where many complex elements begin to form.
The Quadrogram does not actually hold much power, but its four contained Trigrams do.
The Pentagram is a well-known device in Aefian and Human fokelore, as both witchcraft and druidism stem from their appearance. In truth, most magic sources, even the ebb and flow of a planet, work very well in a group of five, and many spalls of both protection and harm can very quickly form in the center hole of the Pentagram.
The Hexagram is powerful, as it symbolises the Trigram of Duograms, where three pairs of elements work together. Origin of the Magic term Hex. (This is probably not true in Real Life)
A Decakilogram, or a Polygram with Ten Thousand sides, is the most powerful of all polygrams above ten, as further than ten is redundant, as it begins to rely on secondary elements, and polygrams above twelve enter impracticality. A Decakilogram, however, holds the symbolic amount of elements as Ten Thousand, and as such represents perfection. It is implied that the Ninth Element is best represented by the Decakilogram, as the Universe itself is a balance of all other elements.