A little-known result in Newton’s Principia Mathematica is that by adding an inverse cube force to the usual force of gravity, you could change the angular motion of a planet while leaving its radial motion unchanged. This can have strange effects, shown in the animation here.
This picture shows part of a graph called the Balaban 11-cage. A (3,11)-graph is a simple graph where every vertex has 3 neighbors and the shortest cycle has length 11. A (3,11)-cage is a (3,11)-graph with the least possible number of vertices. The Balaban 11-cage is the unique (3,11)-cage.