Congruence Testing of Point Sets in 4 Dimensions
  Congruence between two n-point sets in 4 dimension can be checked in O(n log n) time. On the way to establishing this result, we revisit several parts of 4-dimensional geometry, such as angles and distances between planes, Hopf fibrations, and Coxeter groups. 
Heuna Kim and G\"unter Rote
cs.CG