  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, $\overline{{\bf H}_\bh^n}$, up to congruence in the
holomorphic isometry group ${\rm PSp}(n,1)$ of ${\bf H}_\bh^n$. In this paper
we concentrate on two cases: $m=3$ in $\overline{{\bf H}_\bh^n}$ and $m=4$ on
$\partial{\bf H}_\bh^n$ for $n\geq 2$. 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.
