Here are two ornaments, one based on a 432 electron solution to the Thomson problem; the second on a 522 electron solution. See
The coordinates of the electrons were used to create polyhedron duals. Both duals have 24 pentagonal faces and 12 heptagonal faces with the remainder of the faces being hexagonal ones. The heptagonal faces each share edges with 2 pentagonal ones. A heptagonal face, surrounded by 5 hexagonal and 2 pentagonal faces, is clearly shown in the left hand image above. This pattern occurs in solutions to the Thompson problem presented at the above web site and containing more than 400 electrons.
On my Replicator I printed the ornaments using external support.