**If you just want to give this quick try go to the table "make a new repulsion polyhedron"
enter a value and click button "make it" . To avoid delays input values under 20. To see this again refresh the browser screen.**
Imagine points embedded in the surface of a sphere. If they repelled each other where would they end up? How could a collection of such points be described? My Web friend Martin had the idea of representing them as the vertices of a polyhedron.
I liked them a lot but could not see the detail I wanted. Then I color coded the lengths of the edges. Lots of interesting shapes became obvious.

I had expected Platonic solids but they only occured for 4 and 12 vertices. Bipyramids occurred for 5,6,7. A snubbed 4 prism at 8.
9 is a 3 prism with pyramids on each square face. 24 and 48 are weird descendants of the cube. Most of the larger ones are nets of triangles but all have radial or planar symmetry. Spotting the plane or axis of symmetry is tricky but I think there is always one.

If you enter 35 vertices sometimes you get a structure with 46 edge lengths and other times 54 lengths. This often occurs at higher vertice numbers. The structures are quite repeatable. I call them Geometric Isomers.

It works ok on Chrome under Windows10 Other testing is very limited. Avoid 36 vertices if your system is slow. Stay under 20 if it is very slow.
Happy to chat

Bob Allanson Counter