An important problem in quaternionic hyperbolic geometry is to classify ordered m-tuples of pairwise distinct points in the closure of quaternionic hyperbolic n-space, (Formula presented.), up to congruence in the holomorphic isometry group PSp(n,1) of (Formula presented.). In this paper we concentrate on two cases: m=3 in (Formula presented.) and m=4 on (Formula presented.) for n≥2. New geometric invariants and several distance formulas in quaternionic hyperbolic geometry are introduced and studied for this problem. The congruence classes are completely described by quaternionic Cartan’s angular invariants and the distances between some geometric objects for the first case. The moduli space is constructed for the second case. © 2015, Springer Science+Business Media Dordrecht.1801203228NSFC, National Natural Science Foundation of China