dammit i'm trying to learn about quaternions now and I really don't like it

The daisy chain of rabbit holes here is I thought it'd be nice to visualize some of the nested polyhedra stuff I've been working out in 2D and in construction paper models in an actual 3D geometry environment. Using FreeCAD to spawn e.g. a cube and a dodecahedron of appropriate relative size has been very straightforward. Rotating the dodeca to appropriately line up with the cube is my sudden venture into and despair at quaternion rotation.

Like, I can certainly handwavingly explain the sequence of rotations on a couple axes required to rotate the default dodeca into position. But how to communicate that as an angle and three Y, X, Z axis magnitudes is a decidedly brick-wall moment. I need to find an explainer that helps me get an intuitive grasp on this.

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@joshmillard 3b1b has a video on visualizing which you might have seen, but in case you haven't: youtube.com/watch?v=d4EgbgTm0B

Alas, it did little for me. It did increment my intuition on the subject by one unit, but not enough to motivate me to keep banging my head against the wall.

@rook Yeah, just watched that, not really breaking through the wall for me. Reasonably speaking of done very very little stuff with rotation in 3D space to begin with so I don't even really have another model to try and relate from.

@joshmillard I kinda feel the same way, although I've used rotation matrices before, but only in a workaday programming kinda way. I might be able to learn to use them in that capacity, but I don't see the value in that when I can just crib off some notes or a 3D engine or whatever to get the job done.

I have a fear that the deeper understanding I'd like to have just isn't to be found in the subject... like maybe it's somehow shallower than I think? I doubt that, but I still worry.

@joshmillard in case it is at all helpful: Omar Shehata's "Learning to See in 4D" video at bangbangcon.com/2019/recording

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