I'll note that power isn't the only thing coded by the shape. The number of sides is significant in two ways.
Which, Pan, is why I said square and not pentagon, for example.
And to the curious, look on the catalog of nyartefacts on the wiki and spot differences other than power between shapes. It's there, though I knew what I was looking for before I looked.
Would it be possible for you to disclose your theory? Because I cannot see the damned second meaning (even with the first not fully proved) to the shapes. Hmmm. Age of the artifact, perhaps?
Also, what is your stance on circles in the overall shapes system? Mathematician in me screams at placing them below triangles for 'not having enough sides'.
I wonder if the box shape also dictates the severity of the side effects, since boxes of shapes with more sides seem to produce items with more pronounced side effects. Side effects in this case being effects produced in the process of making the device work properly, or as a result of the device's intended function, like Shackle challenges or the void suit attracting Timmy.
As for myself, for some time I've been following a theory that it is the line that determines the fuck-up/user danger potential, with vertical lines being just short of actively malicious artifacts, horizontal ones being mostly benevolent or at least not too dangerous to the user, and diagonal ones being somewhere in the middle, denoting potentially dangerous artifacts, which are, however, not actively harmful to the user by design, only by mistake and misuse. One of the reasons I am still hesitant to check the contents of the Bag, by the way.
No line at all might mean absolutely safe ones, though the evidence is slim; perhaps they are also often somewhat stunted in power compared to the three line-bearing types. Again, not enough evidence.