After watching Interstellar, I thought a lot about the tesseract or hypercube, which I first heard about as a kid reading A Wrinkle in Time, and later encountered on Carl Sagan's original Cosmos. The subject always fascinated me, and why not? I love that I can think about something without really being able to picture it. The three-dimensional "shadow" of the hypercube is the best way to approach understanding it, if you have no math (which I don't). In fact, almost everything on that Wikipedia page I linked to above is Greek to me (in some cases, literally).
rhombic dodecahedron forms the convex hull of the tesseract's vertex-first parallel-projection." I don't know what a rhombic dodecahedron is (I mean, I read the link, but I still don't get it). I'm not sure what a "vertex-first parallel-projection" is, either. As best as I can tell, the rhombic dodecahedron seems to frame a three-dimensional shadow of a four-dimensional tesseract. That's the important point for me. It was a moment of serendipity. Two things that have lurked in my mind since childhood now coalesce. It's not important that I understand the math, or appreciate that a rhombic dodecahedron isn't the same thing as the "perfect solid" dodecahedron with twelve identically-shaped faces. What matters is that in Gonen's World mythology (fictional though it may be), the dodecahedron just got more credibility as a mystical, quasi-magical (or, as we say in Gonen's World, mathemagical) object/concept. If any kind of dodecahedron and the tesseract are connected in any way, even theoretically, I feel like it justifies or legitimizes my fictional concept of the dodecahedron all along. If, in Gonen's World, the dodecahedron is the pathway to "magical" power, maybe it has something to do with it giving the practitioner of such arts a gateway or, better yet, a control panel of sorts to operate in higher dimensions, manipulate space, time and matter, and achieve "magical" effects.
It's not necessary that the "Laws of Nature" in a fictional world be in accord with the laws of the real world. But it is nice when they're somewhat self-consistent, and that's my big discovery here today: more evidence that the dodecahedron was and is the best choice for a mystical symbol of hidden meanings and ultimate truth in Gonen's World.