My world's magic system employs numerous means to cast spells. These include chanting, activation of magic circles, rituals, etc. As the question suggests, my question today is on magic circles.
My world uses typed magic broken down into two categories.
Elemental magic includes Fire, Water, Wind and Earth. So named because these four substances make up most of the world, and so together are dubbed "The Elements".
Arcane magic includes Light and Dark. This magic manipulates both light and shadow, as well as various physical phenomena.
Note that elemental magic only deals with generating or manipulating the elements. For instance, fire magic isn't some abstract generalised form of magic which can absorb kinetic energy or similar. Each elemental magic does only what it says on the box.
Arcane magic on the other hand extends beyond just manipuilating light and shadow, and also deals with concepts such as teleportation, gravity, and other such intangible ideas.
There is no sleep / paralysis / memory manipulation / etc. magic.
All means of casting spells involve 3 components. The only one of which pertinent to the question is the first of the three, seen below.
Definition: This is the drawing of the magic circle itself. The shape of the magic circle has a fixed / defined output, but two different magic circles can have similar effects. This component is subject to a strict set of rules, being logically consistent in relation of definitions (magic circles) to resultant spells.
Relationship Between the Two
I would like each element to be represented by a shape, such that the magic circles for each type of magic are distinguishable from one another. Furthermore, rather than 2D shapes, I would like the true natures of the shapes representing each element to be one of the platonic solids. Ideally, the assignment will be similar to that of Plato, in which the tetrahedron is fire, hexahedron is earth, octahedron is air, and icosahedron is water. I don't mind arcane magic sharing the dodecahedron, but would ideally have a manner for distinguishing one from the other.
Now of course, one can't exactly draw a 3D shape on a 2D plane. As such, I was hoping to use some 2D analogue to represent each of the convex regular polyhedra. (Triangle is tetrahedron, square is hexahedron, etc.)
Note: No magic circle involves text. Solely lines and shapes and always with a circle on the outside. Written text is a symbolic human construct and thus arbitrary. Magic circles only use geometry as a result.
The plan was to represent the tetrahedron, hexahedron, dodecahedron, and icosahedron as a triangle, square, pentagon and hexagon respectively. However, I do not know how I can represent the octahedron. If I take its appearance from a vertex, it looks like a diamond, but there's really no difference between a diamond and square. If I take its appearance from its face, it's a hexagon, but this is the same as the icosahedron.
So my question is, how can my magic circles somehow illustrate the difference between the octahedron and other shapes in 2D, and how can I have both light and dark be represented by a pentagon, but be clearly distinct?