Need help with rotating the sides of a Pyraminx for a Pyraminx simulator.

It's been about two weeks since I started working on this and I haven't been able to figure it out.

Here's how a real-life pyraminx side is supposed to move:

and here's how far I've gotten mine to move:
https://media.giphy.com/media/4vslNT3Y9rRFed6OZU/giphy.gif

So my basic ideas around this were to rotate the sides along the axes of the pieces at the tips. I managed to get the normal vectors of the faces along the pieces located at the tips and used one of those vectors as my rotation axis.
Here's a look at the normal vectors:
https://media.giphy.com/media/uN2LCAHZEbDOExE3Df/giphy.gif

I also managed to get a tip rotating in the right direction, except the rotation was slightly off.
Here's the tip piece rotating:
https://media.giphy.com/media/sZU7kBwcJrhHzKREFe/giphy.gif

If you look closely you can see the rotation is a bit wobbly as if the object isn't rotating around its center.

Here's another video of a real life Pyraminx and the type of rotation I am trying to achieve:

Thanks in advance.