Face to face. I have two examples (although, 2d shapes don't generally have a 'face'.)
2D on a 3D face. Imagine sheet metal plastered on the side of a box
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or
One side (the 2d side) is simply colored in the magic being used. This probably won't make sense for different shapes, unless you make them into something like a triangular prism, etc.
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So there'll be incompatibilities with tiers of magic in a sense. E.g a sphere can't interact or combine with other magic, and probably not even a circle aside from maybe a cone. But this is probably a good thing since in this magic system we're assuming circles are the weakest anyway, so it makes sense in that context.
Basically, your magic system is akin to building blocks. I'm not sure what other things go on underneath the hood, but let's assume that it's simply just these shapes for simplicity sake. You'd have a discipline revolving around these and interactions, so naturally there'll be recognisable or predetermined formulas for magic.
E.g -
Steam magic
The most basic blueprint would be something like this.
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3 triangles arranged like a croissant. Why is this steam?
- 1 triangular polyhedron water w/ 2 triangular polyhedron fires = steam. It could be just the right ratio to create it, but it can be tweaked by better mages. Or better yet, you can add something acidic/acrid to the other two remaining faces (we can connect +4 since the vertices of the shape itself is 4. it'll look like a caltrop for something like an acidic steam cloud.
But this doesn't answer how it determines the function. Just what the magic 'is'. You could have these as a miniature version and used as symbols rather than the shape itself, kind of like a language/inscription. That way you can different iterations of the same principle magic (steam) but it all comes down to who has the better arrangement.
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(Could be interesting to have them as their equivalence of atoms and molecular makeup! Just in magic!)
Or honestly, have magical inscriptions written into the shape itself that determines how it functions rather than the previous suggestion. This is probably the simplest and easiest way. That way you can have some pretty interactions like physically breaking an oponent's 'magic circle' to sabotage it, or the inscriptions to make it malfunction/incomplete.
Also please pardon my Picaso pictures.
No problem! Have fun!
Also to add, if you do go for the inscription route and magic can be interrupted or broken, then it'll make sense for why 4th Dimensional magic 'circles' are God-like because they'd be nigh impossible to break with how they phase between the 3D and the 4D, like moving in and out of reality. Have a look at Ramiel in Neon Genesis Evangelion with how it operates. It's super cool.