Another crazy day and I am so tired. Just got home and read this.
This is what I understood:
As we go across the periodic table atoms/ions have smaller radii (this one is known by everyone). For lanthanides, this decrease in radii cause change in geometry and coordination. So, they prepared series of complexes and investigated the change in their geometry and this fit well with the lanthanide contraction.
For coordination chemistry people, there are a few less common (at least for me) geometries such as "monocapped square antiprismatic" and "dodecahedron."
A beautiful structure.