Gerard Westendorp on Nostr: Lately, I have been making some graphs of N-simplices, they have all vertices on a ...

Lately, I have been making some graphs of N-simplices, they have all vertices on a circle. I was wondering what graphs of the Platonic polyhedra would look like, if you put all vertices on a circle. Well, below an answer.
Actually, there are more than 1 ways to do it. The dodecahedron and icosahedron do not have the same "connectivity" (the number of points on the circle they skip to per edge) for each vertex. I tried to find a way to solve this. It turns out the icosahedron and dodecahedron have a Hamiltonian path (didn't know that!), which would correspond to each vertex being at least connected to its 2 neighbors on the circle.
But these Hamiltonian paths also do not lead to a "symmetric" graph. Maybe it is not possible...