Periodic Solutions with Singularities in Two Dimensions in the $n$-body   Problem
  Analytical methods are used to prove the existence of a periodic, symmetric solution with singularities in the planar 4-body problem. A numerical calculation and simulation are used to generate the orbit. The analytical method easily extends to any even number of bodies. Multiple simultaneous binary collisions are a key feature of the orbits generated. 
Tiancheng Ouyang, Skyler C. Simmons, Duokui Yan