Krystal Guo on Nostr: ah yes, they do look squished to me. The reason is that I’m computing the ...

ah yes, they do look squished to me. The reason is that I’m computing the eigenvalues in SageMath, which is trying very hard to find integer eigenvectors, so there are more 0s than 1s.

Now I think about it, your map of swapping sqrt(5) to - sqrt(5) is just the single nontrivial Galois automorphism of the splitting field of the eigenvalues. This means if I apply it to an eigenvector of -sqrt(5), I should get an eigenvector of sqrt(5).

So now, I’ve computed the eigenvectors in scipy linalg (which gives orthonormal eigenvectors). The eigenvectors of -sqrt(5) give the great icosahedron and of sqrt(5) give the icosahedron. New video.