This 12-body repeating orbit was found by Cristopher Moore and Michael Nauenberg in 2005. They also have a gallery of their orbits.
You can rotate the orbits by clicking in the center and dragging with the mouse. Try dragging down until you see a triangle in the middle, then you can look down at the point. Or drag straight right until you look at the cross of two rings. The numbers in the upper left corner are the number of iterations and the percentage energy lost.
Here it is again, without perspective. This makes the 3-D less obvious but the actual shapes more obvious.
And once more, up close, without trails, and I'll let it go past where it falls apart. And I added a slight error to make it nonsymmetric. Click and drag to rotate.